He did the marriage contract with a girl but did not tell his parents, and he wants to do the marriage contract again in their presence

Praise be to Allah.

Firstly: 

If the first marriage contract fulfilled the conditions and necessary parts, namely the consent of both parties, the presence of the woman’s guardian and the testimony of two Muslim witnesses of good character, then this is a valid marriage contract with all that results from it. But if any of these conditions were not met, then it is an invalid marriage contract and must be repeated. 

Secondly: 

It is no secret that the parents have great rights and should be honoured and treated kindly. Hence it is essential to consult them with regard to the matter of marriage and to strive to please them as much as possible. 

If no obvious negative consequences will result from telling them about the previous marriage contract, then it is better to tell them about that and strive to please them. It is more important to tell them if the wife is pregnant, so as to ward off accusations and suspicion. 

But if telling them will lead to obvious negative consequences, such as the fear that they would sever ties with you and the like, then you can pretend to do the marriage contract in their presence or have it registered officially if it was not registered. 

What is meant by pretending to do the marriage contract is that the guardian of the woman should say: I give my daughter or sister So and so to you in marriage, and you should say: I accept to marry So and so -- in the presence of two witnesses of good character, but you should inform the guardian that this new marriage contract does not really mean anything and that what counts is the first one. 

And Allah knows best.