Do I need to pay tax on foreign dividend both in US and India? Can I claim credit for the taxes paid on such dividend in India?

Yes, tax needs to be paid on Foreign dividend both in US and India. However, an Indian Resident individual can claim Tax credit of taxes paid in US by virtue of Double Taxation Avoidance Agreement (DTAA) entered into between India and US by filing a return of income in India. 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.