Voronoi diagrams are useful for reasoning spatial properties among particles. In particular, the Voronoi diagram of circles in 2D is important on its own and has many applications. And also it is meaningful for extending to that of spheres in 3D. In this paper, we propose a new algorithm for construction of Voronoi diagram of circles. This algorithm constructs the Voronoi diagram by adding a new circle to the already constructed one and then changing the topology influenced by the new circle. The approach using topology uses logical computations instead of numerical computations. That reduces the number of numerical errors.