As a green card holder, you generally are required to file a U.S. income tax return and report worldwide income regardless of the amount and whether or not you receive any forms from the payee. All income is reported on form 1040. Your worldwide income is subject to U.S. income tax, regardless of where you reside.
Also, you maybe eligible for a dollar-for-dollar foreign tax credit on any foreign income tax paid. Subject to various limitations, the amount of tax paid to foreign countries and U.S. possessions on foreign-source income offsets any U.S. tax that would be paid on the same income.
Taken as a deduction, foreign income taxes reduce your U.S. taxable income. File Form 1116 Foreign Tax Credit to claim the foreign tax credit if you are an individual, estate or trust, and you paid or accrued certain foreign taxes to a foreign country or U.S. possession. Or you can chose to deduct foreign taxes on Schedule A (Form 1040), Itemized Deductions
Also, as a US permanent resident, you are also required to file FinCEN Form 114 (an FBAR) if the combined balance of all the foreign accounts you own or have a financial interest or signature authority is more than $10,000 at any point.
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