Abstract: A unified discontinuous Galerkin finite element framework on unstructured grids is developed to simulate gas-liquid twophase flows.In the framework,interior penalty discontinuous Galerkin (IPDG) method is employed to discretize imcompressible Navier-Stokes equations,while Runge-Kutta discontinuous Galerkin (RKDG) method is used to solve Level Set equation.Lid-driven cavity flow is simulated to validate IPDG method.Numerical results of bubble rising indicate the approach can be used to complex twophase flows with low computational efforts and simple implement.Moreover,RKDG method can effectively track deformations of interface without reinitialization.