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.