A three-wavelength passive demodulation technique to interrogate extrinsic Fabry-Perot interferometric (EFPI) sensors with arbitrary cavity length has been developed. The DC component is obtained online, then the applied dynamic signal is recovered by using three new signals without the DC component. The performance of the technique is demonstrated by simulations and experiments. The demodulation technique can extract dynamic signals, regardless of whether the phase modulation is larger than 2π. Theoretically, EFPI sensors with arbitrary cavity length can be demodulated by the demodulation technique, and EFPI sensors with cavity lengths in the 22.96-1002.3 μm range are detected successfully by the same demodulator in experiments. The technique is robust with respect to the bending loss of the leading fiber. The demodulation technique provides a robust and accurate solution to measure dynamic signals for EFPI sensors. It has the properties of high frequency, a large dynamic range, and high sensitivity. The paper demonstrates this technique's potential for measuring dynamic signals.