Abstract: Due to the features of easy implementation and high-efficiency of spectral FDTD, it has been successfully used in periodic structure simulation. To deal with the low efficiency issue in the case of off-normal single angle incident, an improved spectral FDTD is proposed, together with the implementation of GPU acceleration. The improved method reduces overall runtime by modifying spectral resolution requirement of each simulation run while ensuring the accuracy of each frequency response. As is verified in the simulation example, the improved spectral FDTD is at least twice as fast as the original scheme dealing with off-normal single angle incident case, while GPU acceleration offers another 20-fold speed up, that proves the high efficiency of the improved FDTD method with the use of GPU acceleration.