The mid-infrared band(2. 5~25 μm)includes both the characteristic frequency region(2.5~7.7 μm)and the molecular fingerprint region(7. 7~16. 7 μm)，making it ideal for spectral detection and molecular sensing applications. Reconstructive spectrometers based on guided wave optics have demonstrated excellent performance in the near-infrared and visible ranges. However， achieving reconstructive spectrometers with large bandwidth， high resolution， and compactness in the mid-infrared remains a significant challenge. In this study，we developed an on-chip reconstructive spectrometer based on cascaded Fabry-Perot(F-P)cavity filters fabricated on a germanium-on-silicon mid-infrared platform. A waveguide Bragg grating serves as the reflector for each F-P cavity. The spectrometer integrates 63 cascaded F-P filters，selected through a specific algorithm. Simulation indicate a resolution of 0. 4 nm over a 600 nm bandwidth near 4 μm，yielding a bandwidth-to-resolution ratio of 1 500 without any additional tuning.