Efficient implicit predictor-corrector LU-SGS discontinuous Galerkin (DG) approach for compressible Euler equations on unstructured grids is investigated by adding the error compensation of high-order term. The original LU-SGS and GMRES schemes for DG method are discussed. Van Albada limiter is employed to make the scheme monotone. The numerical experiments performed for the transonic inviscid flows around NACA0012 airfoil, RAE2822 airfoil, and ONERA M6 wing indicate that the present algorithm has the advantages of low storage requirements and high convergence acceleration. The computational efficiency is close to that of GMRES scheme, nearly 2.1 times greater than that of LU-SGS scheme on unstructured grids for 2D cases, and almost 5.5 times greater than that of RK4 on unstructured grids for 3D cases.