Diffractive optical elements (DOEs) for beam shaping are widely used in many fields, and there are many kinds of optimization algorithms to design the DOEs for beam shaping. However, only the intensity distribution of the selected sampling points is controlled by these optimization algorithms. The intensity distribution of other points on the output plane is always far away from the ideal distribution. The reason is that the sampling interval on the output plane is not small enough. In this paper, a new modified GS algorithm is presented with a small enough sampling interval on the output plane. A two-dimensional DOE for beam shaping is designed, and the simulation results and the experimental results demonstrate the good performance of this algorithm.