can H1-B visa worker claim an illegal immigrant as a dependent?

You cannot legalize a dependent who is illegal even if you obtain a valid H-1B status for yourself. Your husband would only be able to obtain H-4 dependent status if he left the US, interviewed at an American consulate or embassy, and was issued the visa. I note that most persons who remain in the US illegally for 180 days or one year are barred from returning to the States for three years and 10 years respectively. Due to the limitations of the Lawyers.com Forums, Alan Lee, Esq.'s (the "Firm") participation in responding to questions posted herein does not constitute legal advice, nor legal representation of the person or entity posting a question. No Attorney/Client relationship is or shall be construed to be created hereby. The information provided herein by the Firm is general, and requires that the poster obtain specific legal advice from an attorney. The poster shall not rely upon the information provided herein as legal advice nor as the basis for making any decisions of legal consequence.

He may file for a Tax ID number (ITIN) with the IRS. You can use this number to claim him on your taxes. However, if he is a visitor, you should change his status to a lawful spouse of an H1b, called an H4.