Answer
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
It is not haram to marry a convert at all, but marriage is a serious commitment and you must do your due diligence before proceeding with it.
Answering your question, Sheikh Mustafa Umar, President of California Islamic University, states:
When someone accepts Islam wholeheartedly, their past sins are wiped out. Muslims should always assume the best about people. It is possible that your family is concerned that the man only accepted Islam in order to marry you or is too new to have a solid grounding in Islam.
These are legitimate concerns. It does not make the marriage haram but you should do your due diligence to make sure you are marrying someone suitable for you.
I strongly encourage you to read books and watch seminars about marriage in Islam and to make sure both you and him are ready and compatible.
Many people rush into marriage without preparing for it properly, only to regret it later.
So, in short, it is not haram to marry a convert at all, but marriage is a serious commitment and you must do your due diligence before proceeding with it.
Almighty Allah knows best.