Presented in this paper is an algorithm to compute a Voronoi diagram of circles in a circle, where circles are located in a large circle. Given circles in a large circle, the region in the plane is divided into regions associated with the given circles. The proposed algorithm uses point Voronoi diagram, and then some topological remedies are applied so that we obtain proper initial topology including enclosing circle. From this initial topology, we can obtain the correct topology by a series of edge-flip operations. After getting the correct topology, the equations of edges are computed and represented in a rational quadratic Bézier curve form.