Yes, tax needs to be paid on foreign dividends both in the US and in India. However, an Indian resident individual can claim a tax credit for the same taxes paid in the US under the Double Taxation Avoidance Agreement (DTAA) between India and the US by filing a return of income in India. The maximum credit that can be availed is the amount of tax that should have been paid in India on the transaction if there is no DTAA.
Disclaimer: This article is for informational purposes only. None of the contents of this article should be treated as advice.