She became Muslim but her family do not know and they want her to marry a non-Muslim

Firstly: 

Before answering your question, we would like to congratulate you for becoming Muslim. This is the final religion which Allaah has chosen for all of mankind, and He sent the Prophet (peace and blessings of Allaah be upon him) to be a bringer of glad tidings and a warner to all people. Many of those whom Allaah has guided have entered this religion before you, and many have been deprived of it because of their stubbornness and pride. So you should always be grateful to Allaah for having brought you out of the darkness of kufr and ignorance into the light of Tawheed and knowledge. You have to learn the rulings of Islam so that you will become more convinced of your choice and so that Allaah may make your heart steadfast in adhering to Islam. 

Secondly: 

The fact that you are new in Islam does not prevent us from telling you that this religion brought important rulings by means of which the Muslim can protect his religious commitment, mind, wealth, honour and lineage. Hence there are things that are forbidden in order to protect these things, and there are things that are enjoined for the same reason. There are two things that have to do with your question: 

In order to protect honour and lineage, Islam forbids mixing between the sexes, and it forbids a man to be alone with a woman or to touch her with his hand, let alone anything that is more serious than that, namely the sin of zina (adultery or fornication). Hence we regard a woman as a precious jewel which should not be treated as a cheap product – as is the case in the kaafir nations and the fools among the Muslims who follow them – in advertisements, newspapers and magazines. Women have an important role which awaits them, that of wife and mother. 

The second matter has to do with protecting a woman’s religious commitment. Allaah has forbidden marriage of a Muslim woman to a kaafir man. This is something that is proven in the Qur’aan and Sunnah and by scholarly consensus. 

Shaykh Ibn ‘Uthaymeen (may Allaah have mercy on him) said:  

It is not permissible for a kaafir to marry a Muslim woman, according to the texts and scholarly consensus. Allaah says (interpretation of the meaning): 

“O you who believe! When believing women come to you as emigrants, examine them; Allaah knows best as to their Faith, then if you ascertain that they are true believers send them not back to the disbelievers. They are not lawful (wives) for the disbelievers nor are the disbelievers lawful (husbands) for them”

[al-Mumtahanah 60:10]

It is not permissible for a Muslim woman to marry a kaafir, according to the texts and scholarly consensus, as stated above, even if he is originally a kaafir and not an apostate (from Islam). Hence if a kaafir man marries a Muslim woman, the marriage is invalid and they must be separated. But if he becomes Muslim and wants to marry her, that can only be done with a new marriage contract. End quote. 

Majmoo’ Fataawa al-Shaykh Ibn ‘Uthaymeen, 12/138-140 

Thirdly: 

In order for the marriage contract to be valid, there must be a wali (guardian) for the woman, but it is not permissible for a kaafir to act as the wali of a Muslim woman, and there is no difference of scholarly opinion on this point. 

Ibn Qudaamah said: 

As for a kaafir, he cannot be the wali of a Muslim woman under any circumstances, according to the consensus of the scholars, including Maalik, al-Shaafa’i, Abu ‘Ubayd and as-haab al-ra’y. Ibn al-Mundhir said: There is consensus on this point among all those from whom we acquired knowledge. 

Al-Mughni, 7/71 

Even in a situation such as yours, there has to be a wali for the purpose of marriage. If no one among your family is Muslim, then whoever acts in the stead of the ruler should arrange your marriage for you, namely the Muslim qaadi (judge) or mufti or Shaykh of an Islamic centre or imam of a mosque. 

You do not have to ask your father’s permission to get married because he has no authority over you as a wali. Once the marriage contract is done, it is permissible to keep the news from your parents, and you do not have to inform them. 

Fourthly: 

Even if the wali is a Muslim, it is not permissible for him to force his daughter to marry someone whom she does not like. Islam makes the woman’s consent one of the essentials of the marriage contract, and the contract is not valid if she objects. If it is proven that she objects then the Muslim qaadi should give her the choice between continuing the contract or annulling it. 

Just as it is not permissible for both parents or one of them to force his son to marry someone whom he does not like, so too Allaah has not made the approval of the parents or one of them a condition of the son’s marriage contract being valid. But the son should be kind to his parents if he refuses to do what they want. He has to do his utmost to win their approval of his marriage to the one he wants.  

Shaykh Ibn ‘Uthaymeen (may Allaah have mercy on him) said: 

It is not permissible for a father to force his son to marry a woman whom he does not like, whether that is because of some fault in her religious commitment or a physical defect. How many people have regretted forcing their children to marry women whom they do not want, saying, “You will marry her because she is my brother’s daughter” or “because she is from our tribe” and so on. The son is not obliged to accept, and it is not permissible for the parents to force him. Similarly, if he wants to marry a righteous woman but the father does not want him to, the son is not obliged to obey him. If the son is pleased with a righteous wife and the father says, “Do not marry her,” he has the right to marry her even if his father objects, because the son is not obliged to obey his father in any matter in which that will not harm the father but will benefit the son. If we say that the son is obliged to obey his father in all things, even in matters where there is benefit for the son and no harm for the father, then many negative consequences would result from that. But in situations such as this, the son should be diplomatic with his father, and be kind to him as much as he can and try to convince him as much as he can. End quote 

Fataawa al-Mar’ah al-Muslimah, 2/240, 241 

Fifthly: 

You have to do as much as you can to save your parents and bring them into Islam, so that they and you will find happiness in this world and in the Hereafter. You can use many ways to call them to Islam, such as sending them e-mails, for example, without them knowing that the messages are coming from you. You could give their address to some of those who are specialized in Islamic knowledge and da’wah to undertake this mission on your behalf. You can also avail yourself of the nearest Islamic centre to their home so that some daa’iyahs can visit them and call them to Islam. You can also use the regular mail to send them tapes and booklets that will tell them about the Islamic religion. 

You know more about their situation than others. Perhaps if you tell them that you have become Muslim, that may open the door for them to enter Islam too. If that is the case, then tell them, but if you think that this will not do any good, and that it may have a negative effect on them or it might cause difficulties for you, then do not tell them. You can delay that for a while until Allaah opens their hearts. Seek the help of Allaah and turn to Him with du’aa’, sincerely asking Him to guide them. 

We ask Allaah to make you steadfast in adhering to this religion, and we ask Him to guide your parents to Islam. 

And Allaah knows best.