I am divorced,my ex wife doesn'work,I am paying alimoney,child support and attorney's fees,she claim my son last year and I want to claim my son this year.How the law work in this case and who should claim the child?

Unless there is specific instructions in the custody agreement, most custody agreements spell out who gets to claim on what years. But if there is no agreement in the divorce / custody agreement, then the parent with primary custody gets to claim the child

WaterPolo:

What Fr Chuck says is true, but, based on your posting, her ONLY taxable income is the alimony you pay.

You need to approach your ex-wife and negotiate in good faith about who would best benefit from claiming your son. By modeling BOTH of your returns (using a tax professional who would prepare BOTH returns makes this a simple process), you could mutually agree on how to file and share in the enhanced refunds.

Of course, if she is totally uncooperative, then you are stuck, because she, as the custodial parent, has final say.

But it does not hurt to TRY! All she can do is say NO!