This paper defines and studies the half Bernstein polynomials to approximate functions in C[0,1]. The pointwise convergence in ordinary approximation is given for these polynomials. Also, the order of approximation, the Voronovskaya-type asymptotic theorem and the error estimate are introduced. Finally, to show the ability convergence of these polynomials we provide some examples to approximate these polynomials to test functions and compare numerical results with the results corresponding to classical Bernstein polynomials.