Reverse time migration (RTM) is widely used in the industry because of its ability to handle complex geologic models including steeply dipping interfaces. The quality of images produced by RTM is significantly influenced by the performance of the numerical methods used to simulate the wavefields. Recently, a weighted Runge-Kutta discontinuous Galerkin (WRKDG) method has been developed to solve the wave equation, which is stable, explicit, and efficient in parallelization and suppressing numerical dispersion. By incorporating two different weights for the time discretization, we have obtained a more stable method with a larger time sampling. We apply this numerical method to RTM to handle complex topography and improve imaging quality. By comparing it to the high-order Lax-Wendroff correction method, we determine that WRKDG is efficient in RTM. From the results of the Sigsbee2B data, we can find that our method is efficient in suppressing artifacts and can produce images of good quality when coarse meshes are used. The RTM results of the Canadian Foothills model also demonstrate its ability in handling complex geometry and rugged topography.