In this presentation, a moving mesh discontinuous Galerkin (DG) method is developed for the numerical solution of hyperbolic conservation laws. The method combines the DG method and the mesh movement strategy which is based on the moving mesh partial differential equation approach and moves the mesh continuously in time using a system of mesh partial differential equations. The mesh is a nonuniform mesh that is sparse in the regions where the solution is smooth and more concentrated near discontinuities. The method can not only achieve the high order in the smooth region, but also capture the shock well in the discontinuous region. For the same number of grid points, the numerical solution with the moving mesh method is much better than ones with the uniform mesh method. Numerical examples are presented to show the accuracy and shock-capturing of the method.