Abstract: Based on Maxwells equations, a weakly conditionally stable finite-difference time-domain(FDTD) method for periodic structures is proposed. The stability condition is verified theoretically. Which is looser than that of the conventional FDTD method. And the Sherman-Morrison formula has been used to solve the non-tridiagonal linear system. The new algorithm has better accuracy and efficiency than the ADI-FDTD, especially for large time step size. A numerical example is presented to demonstrate the efficiency and accuracy of the proposed algorithm. Results show the CPU time for this method can be reduced to about 33% of the ADI-FDTD method.