The fast Fourier transform (FFT) demodulation method conbined with chirp Z-translation (CZT) is adopted for Fabry-Pérot pressure sensors and its principle and error are analyzed theoretically. In the simulation, cavity lengths from 397 to 403 μm with the space of 0.5 μm are simulated. The result shows that the relative error by this new method is less than 0.01% and the maximum absolute error is less than 0.05 μm. In the experiment of the demodulation of the MEMS Fabry-Pérot pressure sensor, whose metrical range is from 0 to 3 MPa, its resolution reaches 0.01 MPa, its linearity between the length of the cavity and pressure achieves 0.99316 and the standard deviation between measured pressures and real pressures is less than 0.005 MPa. Experiments show that this new method adapts to the practical demand with higher resolution and less calculation consumption.