As long as you pay your taxes as per your original H1 income you are good to work part time anywhere. Just make sure you pay your taxes according to your original employer's pay stub.

Thanks for the reply, but u actually confused me. I am fine with the paying tax. but what is that 'your original H1 income'. Isn't the tax is calculated based upon your income, what do u mean by h1 income ?? And also from this line 'pay your taxes according to your original employer's pay stub'. If I work for both place, then I will have two pay stubs ?? really confused

You need to file h1 with new company as well.adhikari bandu is wrong.

Your new employer should petition h1 on your behalf and get accepted before you can start working there. No change of H1 is required.

ark bro is right but adikari bandu is wrong.