A novel fiber sensor for the refractive index sensing of seawater based on a Mach–Zehnder interferometer has been demonstrated. The sensor consisted of a single-mode fiber (SMF)–no-core fiber (NCF)–single-mode fiber structure (shortened to an SNS structure) with a large lateral offset spliced between the two sections of a multimode fiber (MMF). Optimization studies of the multimode fiber length, offset SNS length, and vertical axial offset distance were performed to improve the coupling efficiency of interference light and achieve the best extinction ratio. In the experiment, a large lateral offset sensor was prepared to detect the refractive index of various ratios of saltwater, which were used to simulate seawater environments. The sensor’s sensitivity was up to −13,703.63 nm/RIU and −13,160 nm/RIU in the refractive index range of 1.3370 to 1.3410 based on the shift of the interference spectrum. Moreover, the sensor showed a good linear response and high stability, with an RSD of only 0.0089% for the trough of the interference in air over 1 h.