Robust and fast computation of the exact Voronoi diagram of circle set is difficult. Presented in this paper is an edge-flipping algorithm that computes a circle set Voronoi diagram using a point set Voronoi diagram, where the points are the centers of circles. Hence, the algorithm is as robust as its counterpart of point set. Even though the theoretical worst-case time complexity is quadratic, the actual performance shows a strong linear time behavior for various test cases. Furthermore, the computation time is comparable to the algorithm of point set Voronoi diagram itself.