A high sensitivity optical fiber gas pressure sensor based on the enhanced Vernier effect is proposed. The sensor is composed of a fiber Fabry-Perot interferometer (FPI) and Mach-Zehnder interferometer (MZI). Since the interference fringes of FPI and MZI drift in the opposite direction with the change of gas pressure, when their free spectral ranges are similar, the enhanced Vernier effect is formed after their cascading. Compared with the traditional Vernier effect gas pressure sensor, the enhanced Vernier effect gas pressure sensor realizes much higher sensitivity gas pressure measurement without complex manufacturing process or desensitized reference interferometer. The experimental results show that the sensitivity of the enhanced Vernier effect sensor is 241.87 nm/MPa. In the two traditional Vernier effect gas pressure sensors formed by cascading FPI and MZI, the sensitivity of sensor is 63.02 nm/MPa and 171.26 nm/MPa, respectively. Compared with the two traditional Vernier effect sensors, the sensitivity of the enhanced Vernier effect sensor is increased by 3.8 times and 1.4 times, respectively. The proposed sensor also has the advantages of good repeatability and stability, fast response, low cost and easy manufacture. Our structure also provides a new design scheme for a high sensitivity optical fiber gas pressure sensor.