Abstract: NGFMN-K code was developed to solve transient neutron diffusion equations. Nodal Green’s function method based on the second boundary condition was utilized for spatial discreteness. Backward Euler (BE) and a fourth-order accurate diagonally implicit Runge-Kutta (DIRK) method were used for temporal discreteness. Automatic time step control was achieved by embedding a third-order accurate Runge-Kutta solution to estimate the truncation error for DIRK. Numerical evaluations show that results of two methods agree well with reference solution, and DIRK is more accurate and efficient than BE, especially in severe transient.