Interferometric fiber-optic hydrophones are an important means in the field of underwater acoustic detection. The design of the hydrophone sensor head is the key technology related to its detection sensitivity. In this paper, a high-sensitivity cuboid interferometric fiber-optic hydrophone based on planar rectangular film sensing is proposed, and the sensitivity of the sensor is compared with that of the widely used air-backed mandrel hydrophone under the same conditions. The acoustic characteristic models of the two types of sensors were established by theoretical calculation and simulation analysis to obtain the theoretical pressure sensitivity. Some experiments were performed to examine the theory and design. According to the experiment results, the mean phase sensitivity of the mandrel type was −112.85 dB re 1 rad/μPa in the operating frequency range of 10–300 Hz, and that of the cuboid type was −84.50 dB re 1 rad/μPa. The latter was 28.35 dB higher than the former was. These results are useful for improving hydrophone sensitivity.