You will be taxed in the US on your worldwide income. That includes your income in India. You will also have to file additional paperwork due to your ownership of a foreign (to the US) entity, and the corporate income will be taxed somewhat aggressively.
That said, India and the US have a tax treaty which covers variety of issues related to the taxation of Indian residents/corporations in the US. You should find a tax adviser licensed by a US State as a CPA, or by the Federal government as an EA, and who is familiar with the Indo-US tax treaty, to advise you on your issue.
Generally, foreign income tax paid on income derived in India is credited towards your US tax liability on that money, but it may not be a dollar for dollar credit. The tax treaty may help reducing or eliminating your double taxation concerns.