I have a H1b since 2004, but in 2006 a moved with a girl and she has 2 kids, she didn't work the entitle year, so I supported her kids financially the whole year in 2006, My question is, Can I file my taxes and put the kids as Dependants for 2006 with my H1b status?

Thanks,

Since you were on H-1 for ALL of 2006, you will file as a reisdent alien and file Form 1040,

Further, since (I assume) you provided over half the support of both children and their mother, and since they lived with you (I assume you paid the rent), and simce (I assume) the mother did not earn at least $3,300 in income, you can claim the children AND the mother as dependents.