Abstract: In this paper, the principle of discontinuous Galerkin time domain (DGTD) based on vector basis function is described. Weak solutions and matrix formulations from Maxwell equations are given, and the leapfrog equations are presented. The resonant frequencies of the resonator which contains vacuum and a medium plate are calculated respectively by DGTD. The numerical results which are compared with analytical solutions show that the DGTD technique could achieve high accuracy in dealing with resonator problems.