Fabry–Perot (F–P) tunable filter based on micro-electro-mechanical system (MEMS) was widely used in optical communication, laser, and optical imaging. At present, there is little research on F–P filters in the near-infrared band from 1 260 nm to 1 620 nm. Therefore, this paper designs a novel F–P filter based on MEMS. Three improved cantilevers beam circular bridge deck structures, including circular holes, V-shaped grooves, and square grooves, were analyzed through finite element simulation. The voltage-displacement, von Mises stress, and mirror flatness were obtained to select the optimal bridge deck structure. The results show that when different bridge decks reach the same displacement, the voltage required by the square grooves cantilever beam bridge deck is the smallest, and the von Mises stress and mirror flatness of the square grooves bridge deck structure can also meet the design requirements of the filter. Finally, the filtering performance of the optimized square grooves bridge deck structure filter is analyzed.