A fast real-time demodulation method based on the coarsely sampled spectrum is proposed for transient signals of fiber optic extrinsic Fabry-Perot interferometers (EFPI) sensors. The feasibility of phase demodulation using a coarse spectrum is theoretically analyzed. Based on the coarse spectrum, fast Fourier transform (FFT) algorithm is used to roughly estimate the cavity length. According to the rough estimation, the maximum likelihood estimation (MLE) algorithm is applied to calculate the cavity length accurately. The dense wavelength division multiplexer (DWDM) is used to split the broadband spectrum into the coarse spectrum, and the high-speed synchronous ADC collects the spectrum. The experimental results show that the system can achieve a real-time dynamic demodulation speed of 50 kHz, a static measurement root mean square error (RMSE) of 0.184 nm, and a maximum absolute and relative error distribution of 15 nm and 0.005% of the measurement cavity length compared with optical spectrum analyzers (OSA).