In the present paper, we develop a local discontinuous Galerkin (LDG) method  with a high order time stepping scheme for a time tempered fractional diffusion equation. Instead of solving the present model directly, we first transform it into a diffusion equation with Caputo fractional derivative. Then, the full-discrete LDG is constructed by using the L1-2 time stepping scheme to approach the Caputo fractional derivative, and using the discontinuous Galerkin to approximate the space derivative. We prove that the full-discrete discontinuous Galerkin method is unconditionally stable with the optimal convergence rate. We present two numerical examples to illustrate the accuracy and the robustness of the numerical method proposed in this paper. Our experimental results show that the high order accuracy of the present numerical scheme are obtained in both time and space variables.