I want to know if my husband wants to give up his parental rights without his ex wife consenting is that possible? He hasn't seen the child in over a year.

No, and in most cases he can not give them up even with her permission unless she has a new partner to adopt. The custodial parent can "take" away the rights for some specific issues but even that is restricted.

So why does he not see the child ? If he has visitation, he has rights to see, and can use the courts to force visits.