Radial basis function network method is presented for demodulation of Fabry-Pérot pressure sensors, and its principle and error are analyzed theoretically. At first eigenvalue is extracted from interference spectrum, and with the eigenvalue of the spectrum and the length of the cavity the radial basis function network is trained. The trained network can forecast cavity length. In the experiment of demodulating MEMS Fabry-Pérot pressure sensor with metrical range from 0 to 2 MPa, its resolution reaches 0.1 MPa, and the linearity between the length of the cavity and pressure achieves 0.98858. In the simulation, the relative error of this new method is just 0.02% and the maximum absolute error of the length of the sensor cavity is less than 0.1 μm. The experiments show that this new method meets the practical demand with its high resolution.