The existing algorithms of circle clipping against an arbitrary polygon window suffers from complex steps and do not consider the case where the polygon contains an inner ring. Thus, this study presents a new algorithm based on the parameter analysis of intersection points for circle clipping against an arbitrary polygon window. In this algorithm, only by comparing the parameter values of the intersection points on the directional line of the edge, one can classify the intersection points into entry points and exit points. After the intersection points are sorted out, the arcs within the clipping window can be obtained with the combinations of “entry point $\Rightarrow $ exit point.” The proposed algorithm is proved feasible by programming results and is universal to circle clipping against an arbitrary polygon window, even if the polygon contains an inner ring.