I am partner with firm, in India. My share is 25%. As per Indian Tax law, the firm required to pay tax at 30% (Maximum Rate) on firm's total Income. The partner need not required to pay Income-tax in India again on their share of Profit.

My question whether the Share of Profit earned by Me in India, again require to pay tax in USA? It it is so then I am paying 30% tax in India and once again paying 40% tax in USA, is it correct?

If you are a resident of the United States, either as a resident alien or a green card holder, that partnership income IS subject to federal (and probably state) income taxes.

Now, you will be able to offset the added tax by claiming the Foreign Tax Credit to get a credit against the staxes you are paying to India.