Because the spectrum of the interference optical signal in optical fiber Fabry-Pérot (F-P) sensor is sparse, the traditional fast Fourier transform (FFT) algorithm needs to calculate the spectrum components in the whole frequency range in the process of solving the cavity length, and the calculation speed is slow. While sparse fast Fourier transform (SFFT) algorithm only needs to calculate the main spectrum components of the interference optical signal. Through rearranging spectrum, filtering with window function, down sampling in frequency domain, and finally looping location and valuation, SFFT can quickly calculate the K maximal Fourier coefficients of the signal spectrum. Thus SFFT can quickly find the frequency corresponding to cavity length and demodulate the cavity length. The algorithm is simple in structure and low in time complexity. It is verified that the accuracy of the demodulation results of SFFT algorithm is better, and the efficiency is faster than that of FFT algorithm by analyzing the actual interference optical signal of optical fiber F-P sensor demodulation system. It is proved that SFFT is very suitable for on-line real-time demodulation of cavity length of optical fiber F-P sensors, so as to measure physical quantities in real time.