The traditional intensity demodulation method for fiber Fabry-Perot interferometric (FPI) sensors suffers from high error and limited reliability due to light source fluctuation, fiber perturbation, fiber attenuation, and temperature-induced quadrature-point drift. To address these issues, a high-stability quadrature-point demodulation technique is proposed that utilizes wide-and-narrow band ratio processing to suppress the influence of optical system noise and employs an active quadrature-point control technique to eliminate the sensor's temperature-induced zero-point drift. The experimental results demonstrated excellent temperature stability: the demodulation non-linearity error for the FPI sensors did not exceed 1.5% within 25-300°C. The demodulation error was maintained below 1%, even under conditions of optical fiber attenuation introduced by fiber bending, where the radius was no less than 10 mm. This technique successfully overcomes the intrinsic drawbacks of traditional intensity demodulation, retaining its inherent advantages such as a simple architecture, high multiplexing capacity, and high-speed demodulation, while simultaneously achieving superior environmental adaptability and measurement stability for demanding engineering applications.