Conventional shadow mapping algorithm is restricted by the resolution of the shadow map, so aliasing will occur at the edge of the shadows when the resolution of the shadow map is not high enough. To address this problem, this paper presents a new pre-filtering anti-aliasing algorithm based on the high-order power function approximation of the conventional binary-value depth test function. The high-order power function is then approximated by the Taylor expansion which can be further pre-filtered for each of the items. The final shadow value is generated with the first several items of the Taylor expansion. Experimental results show that the algorithm can be used to achieve good results with the current graphics hardware.