We present a high-accuracy fiber-optic Fabry-Pérot (F-P) sensor capable of simultaneously measuring the temperature and gas refractive-index (RI). The sensor consists of a silicon F-P cavity for temperature sensing and a glass F-P cavity with a side groove for gas RI sensing. Two F-P cavities are simply fabricated and connected in series by microelectromechanical system (MEMS) techniques. The hybrid F-P sensor produces a superposition of signals. Changes in temperature and RI can be separated and detected by a fast Fourier transform (FFT) and the wavelength-tracing method. The experimental results demonstrate that the sensitivities of the proposed sensor are 80.7 pm/°C from 10 °C to 60 °C and over 1535.8 nm/RIU in the gas RI range of 1.0000248-1.0007681. Furthermore, the gas RI measurement reaches a high accuracy of ± 7.6 × 10-6 RIU, owing to the temperature compensation. In addition, the measured precisions of the temperature and gas RI are 1.07 × 10-3 °C and 2.73 × 10-8 RIU, respectively.