Most crimes are not an issue if it is on the US citizens record. I suggest you speak with an immigration attorney for more information. My firm is experienced in criminal immigration law and spousal based applications.
Whether this will be a problem depends on how many convictions he has, for what crimes, and the sentences that were imposed.
It depends on what the crimes are and whether it is the beneficairy or Petition that has the record. This is only one of many important considerations in a Marriage based Green Card case.