A highly sensitive optical fiber gas pressure sensor with temperature monitoring is proposed and demonstrated. It is based on a slightly tapered fiber with an inner micro-cavity forming an in-fiber Mach–Zehnder interferometer (MZI), and a micro-channel is drilled into the lateral wall of the in-fiber micro-cavity using a femtosecond laser to allow gas to flow in. Due to the dependence of the refractive index (RI) of air inside the micro-cavity on its gas pressure and the high RI sensitivity of the MZI, the device is extremely sensitive to gas pressure. To prevent fiber breakage, the MZI is housed in a silicate capillary tube with an air inlet. Multiple modes are excited by slightly tapering the inner micro-cavity, and the resonance dips in the sensor’s transmission spectrum feature different linear gas pressure and temperature responses, so a sensitivity matrix algorithm can be used to achieve simultaneous demodulation of two parameters, thus resolving the temperature crosstalk. As expected, the experimental results demonstrated the reliability of the matrix algorithm, with pressure sensitivity reaching up to ~−12.967 nm/MPa and temperature sensitivity of ~89 pm/°C. The features of robust mechanical strength and high air pressure sensitivity with temperature monitoring imply that the proposed sensor has good practical and application prospects.