The high-precision finite volume method (FVM) and discontinuous Galerkin method (DGM) were compared in different test cases through numerical examples. Results show that:with the same precision, the calculation error of DGM is obviously less than that of FVM; DGM's reconstruction process is comparatively simpler than FVM's, but its computational time is much longer since its freedom-degree of polynomial solution is higher under the condition of high order and it needs to calculate volume points. Decreasing the freedom-degree numbers of polynomial solution in the time evolution process is an essential method for high-precision calculation in the reality applications.