If I pay tax in US still I have to pay tax in India?

This forum is for US tax questions.
Anyway, most countries have regulations to avoid double taxation, so if you pay taxes on your income in one country you can take a credit for foreign paid taxes in the other country you are filing a return.
If you want more details for taxation in India, you can ask in this forum http://mytaxes.in

Redundant post.

What TaxesForAlien says is essentially true, but income earned under a J-1 visa as a visiting professor is tax-exempt in BOTH countries under the U.S.-India Tax Treaty. That is probably the underlying reason why there is a two-year cap on the duration of the stay in the treaty itself.