The compressible two-phase flow problem is numerically solved based on the high order discontinuous Galerkin method. The calculation area is divided into unstructured grids， the Euler equation and the Level Set equation are solved iteratively by Newton method and Runge Kutta method， respectively. And the unified algorithm is used for data exchange to realize the solution of the Level Set equation in the compressible flow field under the unified framework. Finally， the algorithm developed in this paper is validated by a classical 2-D example. The Zalesak disk and other examples are given to verify the high resolution of algorithm， mass conservation and advantages in dealing with large deformation problems. Then， the numerical simulation of left-running shock wave by helium bubble verifies the high accuracy of the algorithm in capturing the complex shape of the two-phase flow interface in the flow field.