We perform the topology optimization for the cross-section of WGM ring resonator using the axisymmetric finite element method proposed in (M. Oxborrow, Traceable 2-d finite-element simulation of the whispering- gallery modes of axisymmetric electromagnetic resonators, IEEE Trans. Microw. Theory Tech. 55 (6) (2007) 1209-1218.). The optimization targets are maximization of the Q factor and minimization of the mode volume.