This article introduces an ocean pressure sensor characterized by its heightened sensitivity, employing an elastic diaphragm coupled with femtosecond fiber Bragg grating (FS-FBG) technology. The sensor securely embeds a high tensile strength FS-FBG at the center of an elastic diaphragm and seals it within a sealed chamber, allowing for precise temperature compensation using an additional FBG. This approach effectively prevents chirping phenomena caused by FBG attachment to the diaphragm surface and resolves sensitivity issues associated with metal encasement. This article elucidates and derives the principles of membrane stress deformation based on elasticity mechanics, establishing a linear relationship between the wavelength shift of the FBG and pressure values. A sensitivity analysis of the sensor is conducted, and the sensor's design structure can further amplify the measurement range and sensitivity by adjusting geometric dimensions and mechanical parameters. Feasibility is verified through finite-element simulations and experiments. The sensor fabricated in this study exhibits a sensitivity of 14.66 pm/kPa and achieves a resolution of 0.05 kPa, a fitting coefficient of 0.9999, and a repeatability error of 0.0052% within the pressure range of 0-600 kPa. This provides an advanced and efficient means for high-precision monitoring of seawater pressure.