Can I start a company on H1B visa?

Aliens currently in the United States are allowed to launch businesses like anyone else but they cannot take paid employment with the firm.  It should not be a problem to work in the business during your free time as long as you are not on the payroll.  However, employees can be hired to perform business functions and any profits generated can be legally yours.  You will simply list those profits on your tax return by claiming them as investment returns.  Since this is a complicated matter, I suggest that you seek the help of an immigration attorney and a competent accountant with experience in taxes.