It depends on the state you attend school in. Some states like Illinois do not require a H.S. diploma, but you may have to take an additional test to be admitted. Other states like Montana require students to either have a high school diploma or G.E.D.
You can go to http://www.beautyschool.com/ and click on your state and find the local Cosmo Schools in your state and give one a call and find out for sure what your state requirements are