To analyze the stability of the local discontinuous Garlerkin method for heat equation，where thetime discretization is the explicit TVD Ｒunge-Kutta method. For the sufficiently smooth solution case，when thefinite element space is the k-th order piecewise polynomial space on the regular meshes，we use the finite elementanalysis technique to proof the L2-norm stability for hear equation under the CFL condition τ≤λμ － 2h2，where τ，hare the time step and the length of the element respectively，and μ，λ are constants independent of h，τ.