© 2015 IEEE. This letter proposes a new algorithm for solving the optimal zero-forcing beamforming problem that maximizes the user achievable rate with restriction on the per-antenna element power constraints. An accelerated gradient method with step size search is proposed for solving the problem. For each iteration of the gradient approach, a quick one dimensional search is employed to obtain the step size. The advantage of the step-size search is that it is relatively fast and requires only a few calculations of the objective function. Design examples show that the proposed algorithm converges faster than the gradient approach and the accelerated gradient approach with a constant step size while achieving a low computational complexity.