Based on the method of matrix decomposition and expanding the rectangular function into a sum of complex Gaussian functions and the Collins diffraction integral formulae, the propagation characteristics of a Gaussian beams passing through spatial filter are studied. As a result, corresponding analytical formulae are obtained respectively. By using the numerical method, the analytical formulae are numerically simulated and the results can be got from the simulated figure. Numerical calculations have shown the dependence of the optimum pinhole size on the truncation parameters of the beams. As further extension , numerical calculations are performed for Gaussian beams and flattened Gaussian beams (N=12) propagating in spatial filter of B=0. The relation of truncation parameter and intensity distribution of Gaussian beams passing through filter is obtained.