A novel discontinuous Galerkin time domain (DGTD) method based on compressive sensing (CS) is proposed to accelerate the analysis of electromagnetic characteristics of cavity devices. In the method, a nodal basis function and a leapfrog scheme are used for the spatial and time discretization of Maxwell equations. Meanwhile, all elements in the computation domain are updated individually by applying the conventional method at the initial stage for electromagnetic field updating. When the electromagnetic wave covers the whole domain, all elements are updated as a whole and a global solution is conducted. First, the underdetermined equations are established by randomly extracting rows from the global mass matrix. Second, the results after a few previous time steps are taken as the prior knowledge to construct a sparse transform. Finally, the underdetermined equations are solved by the recovery algorithms to realize the fast analysis of electromagnetic characteristics of cavity devices.