A temperature-insensitive all fiber Fabry–Pérot (F–P) and Mach–Zehnder (M–Z) hybrid compact structure and its sensing characteristics are proposed and theoretically and experimentally demonstrated. In one sensor, two kinds of sensing principles are existing, which is shown in the sensing process that with the increase in the refractive index (RI) of the liquid, the dip wavelengths coming from the F–P interference do red-drift, and the dips from the M–Z interference do blue-drift, respectively. Due to the opposite shift and almost the same temperature sensitivities, the dip difference between M–Z and F–P refractometers is used to eliminate temperature cross-sensitivity and improve the RI sensitivity of the sensor. In our experiments, the liquid RI sensitivity is 134.383 nm/RIU, and temperature cross-sensitivity is effectively eliminated within the ±21.74 °C change range at room temperature. This sensing structure also has advantages of simple structure, good integration, and low power loss.