Based on the classical finite difference method, the paper discusses the construction of a high accuracy difference scheme for the KdV equation with periodic boundary conditions. By introducing an intermediate function and a compact method to discretize the space area, a two-layer implicit compact difference scheme for the KdV equation is proposed. Using the Taylor expansion method, we show that the proposed scheme has second order accuracy in time direction, but can reach sixth order accuracy in spatial direction. The linear stability analysis method proves the scheme is stable. Numerical results show that the compact difference scheme proposed in this paper is effective, it has high accuracy in the spatial direction, and can also keep the conservations of momentum and energy well.