For the problem of the circle clipping against arbitrary polygon window, the more comprehensive and effective clipping algorithm is proposed in this study. First, according to x-scan line algorithm, the spatial relationship between the circle and the polygon window is determined. Next, for the case of the polygon window and the circle intersection, the intersect points of the circle and each side of the polygon window are calculated in the counterclockwise direction and sorted correctly. At last, according to the relationship between two points, determining to draw a line or a circle arc. The whole circle clipping is obtained. The result expresses that the algorithm can be comprehensive and effective to complete circle clipping.