In order to complete the seismic analysis of thirty meter telescope (TMT) tertiary mirror cell assembly (M3CA), seismic wave fitting software has been developed, seismic time histories are obtained through the software, and then seismic analysis has been done based on time history analysis. The software fit for the seismic wave is developed based on the theory of trigonometric series with random phase, amplitude correction is introduced to increase the fitting precision, the average difference between fitting seismic wave spectrum and design response spectrum is less than 4%; then, according to the design response spectrum with average return period of 200 years, seismic time histories are fitted; finite element method (FEM) analysis is carried out based on time history analysis method. The simulation results illustrate that the displacement of tertiary mirror relative to the cell is 1.881 mm; the maximum stress on the mirror is 0.27 MPa which occurs on lateral supporting position; the maximum stress of the support system is 310.54 MPa and appears on the lateral support rod. Compared with material characteristics, the maximum stresses are all within material stress limitation, which indicates that the security will be assured when 200-year return period earthquake happens. The program obtains a high fitting precision and various factors are considered. Combined with the finite element analysis, it will provide experience for seismic analysis of large photoelectric equipment.