An Implicit Reconstructed Discontinuous Galerkin method, IRDG (P 1 P 2 ), is presented for solving the compressible Euler equations on tetrahedral grids. In this method, a quadratic polynomial (P 2 ) solution is first reconstructed using a least-squares method from the underlying linear polynomial (P 1 ) DG solution. By taking advantage of the derivatives in the DG formulation, the stencils used in the reconstruction involve only von Neumann neighborhood (adjacent face-neighboring cells) and thus are compact and consistent with the underlying DG method. The final P 2 solution is then obtained using a WENO reconstruction, which is necessary to ensure stability of the RDG (P 1 P 2 ) method. A matrix-free GMRES (generalized minimum residual) algorithm is presented to solve the approximate system of linear equations arising from Newton linearization. The LU-SGS (lower–upper symmetric Gauss–Seidel) preconditioner is applied with both the simplified and approximate Jacobian matrices. The numerical experiments on a variety of flow problems demonstrate that the developed IRDG (P 1 P 2 ) method is able to obtain a speedup of at least two orders of magnitude than its explicit counterpart, maintain the linear stability, and achieve the designed third order of accuracy: one order of accuracy higher than the underlying second-order DG (P 1 ) method without significant increase in computing costs and storage requirements. It is also found that a well approximated Jacobian matrix is essential for the IRDG method to achieve fast converging speed and maintain robustness on large-scale problems.