Fiber-optic Fabry-Pérot sensors have a wide range of applications, including aerospace, large-scale construction, oil collection, and many other fields. In many cases, dynamic parameters, such as dynamic pressure, vibration, acoustics, and ultrasonics are required to be measured. In order to measure these parameters, a variety of fiber-optic Fabry-Pérot sensors are produced. In some fields, the multi-cavity fiber-optic Fabry-Pérot sensor is inevitable for some advantages. For example, in the field of aerospace engine testing, dynamic pressure is a key parameter that often needs to be measured, and the micro-electro-mechanical system external Fabry-Pérot interferometer pressure sensors with multiple Fabry-Pérot cavities are often designed for aerospace engine pressure measurement due to their consistency and airtightness. Moreover, multi-cavity Fabry-Pérot sensors are good candidates for multi-parameter measurements. The different Fabry-Pérot cavities with different lengths are used to measure different parameters to achieve multi-parameter measurement. Therefore, multi-cavity Fabry-Pérot sensors are becoming increasingly important in engineering applications. However, extracting dynamic signals in multi-cavity Fabry-Pérot sensors is a challenge. In this paper, an improved passive three-wavelength phase demodulation technology based on a broadband light source is proposed for dynamic interrogation of the shortest cavity in a multi-cavity Fabry-Pérot sensor. According to the principle of low coherence interference, when the optical path difference introduced by the Fabry-Pérot interferometer is less than the coherent length received by the photodetectors, interference occurs. In contrast, when the optical path difference introduced by the Fabry-Pérot interferometers is longer than five times the coherence length, the interference phenomenon becomes insignificant and it can be considered that the interference disappears. Therefore, a flat-top amplified spontaneous emission light source and three broadband fiber filters were used to ensure the interference only occurs in the short cavity. The quadrature signals are obtained by three filtered optical signals with arbitrary cavity length using an improved phase calibration algorithm. The established signal calibration algorithm allows the demodulation technology for arbitrary short cavity lengths and arbitrary central wavelength. The demodulation technology can work without the direct-current voltages, so the demodulation system can reduce the fiber-optic disturbance noise. The arctangent algorithm is established to extract vibration signals by the quadrature signals. Compared with the previous phase calibration algorithm, the phase calibration algorithm proposed in the paper is more concise. The experimental system was consisted of a reflective bracket, a light source, a multi-cavity Fabry-Pérot interferometer, a fiber-optic coupler, three fiber filters, three photodiodes, an analog-to-digital conversion and a personal computer. The light from the light source passed through the fiber-optic coupler to the multi-cavity Fabry-Pérot interferometer. A multi-cavity Fabry-Pérot interferometer consists of a gradient-index lens and a 300-μm-thick double-polished quartz glass fixed on a piezoelectric transducer. The light reflected from the interferometer passed through the coupler and through the filters to the photodiodes. Three interferometric signals at each center wavelength were obtained using three photodiodes. The voltage signals were collected by analog-to-digital conversion and transmitted to a personal computer. The feasibility of the demodulation algorithm was verified by simulations and experiments. The experimental results show that the vibration signals with a frequency of 1 kHz and peak-to-peak amplitude of 2.6 μm is successfully extracted with different Fabry-Pérot cavity length, which proves that the three-wavelength demodulation algorithm can be used for optical fiber multi-cavity Fabry-Pérot sensor with arbitrary short cavity length. The demodulation speed is 500 kHz and the demodulation resolution is 0.25 nm. The demodulation technology makes it possible to extract dynamic signals in a multi-cavity Fabry-Pérot sensor. If the spectrometer is used at the same time, the dynamic signal measured by the short cavity and the static signal measured by the long cavity can be interrogated at the same time. This demodulation technology has the advantages of a compact system, low cost, fast speed and high robustness, illustrating its bright potential for multi-cavity Fabry-Pérot sensors.