In this study, the symplectic multi-resolution time-domain (S-MRTD) algorithm is introduced in numerical simulation calculations of photonic crystals to address the problems of low calculation accuracy and large dispersion error in the traditional finite-difference time-domain (FDTD) method. First, the symplectic sub-technology and approximate difference of wavelet scale function were introduced into the S-MRTD algorithm in time and space, respectively. Next, based on the time-reversible constraints and growth factors, a set of optimized symplectic operators was solved. Further, the stability and numerical dispersion of the traditional FDTD method and S-MRTD algorithm were discussed. Finally, based on the S-MRTD algorithm, the transmission and reflection coefficients of photonic crystals were analyzed. Numerical calculation and simulation results verify the feasibility and accuracy of the S-MRTD algorithm. The successful application of the S-MRTD algorithm facilitates a new numerical calculation technique with high accuracy and efficiency for elucidating the transmission characteristics of photonic crystals.