Abstract: In finite element analysis, the generation of quadrilateral(quad) meshes is harder than that of triangular meshes, especially on planar regions with complicated shape and topology structure. In this paper, we developed an iterative method to produce quad meshes on n-sided connected planar regions with complicated geometric shape and high genus, and the generated quad mesh is guaranteed to be non-self-overlapping. Starting with an initial quad mesh, which is constructed by adaptive pixelization, the boundary of the quad mesh is iteratively fitted to the boundary of the given planar region. After each iteration of the boundary, the positions of inner vertices are changed by the layered Laplace operation. Finally, the quad mesh is generated by further optimizations. In the iterations, the movements of the mesh vertices are restricted so that the produced quad mesh is guaranteed to be strictly non-self-overlapping. Lots of examples presented in this paper show the efficiency and effectiveness of the developed method.