Abstract: A curved-boundary based discontinuous Galerkin (DG) method is developed for solving three-dimensional compressible Euler and N-S equations on hexahedral grids. In this method, the quadrilateral face elements are reconstructed to be curved with polynomial interpolation approach, which is better to represent the real boundary. With high-order volume elements clustering only around the boundary surface, this method is easy to implement and requires a small amount of extra computations. Numerical experiments on a variety of flow problems demonstrate that DG method can obtain high-order accurate solutions on relatively coarse grids with the presented curved boundary representation approach. It is worth noting that with an implicit time integration method, converging solutions can be achieved within several time steps.