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This paper presents a theoretical model of lossy mode resonance (LMR) prism refractive index sensor based on the SBS (sensing medium/black phosphorus/sensing medium) structure. By using the sensing medium as the matching layer and the black phosphorus (BP) as the lossy layer, the sensor’s performance under angular interrogation is effectively improved. In addition, the implications on the reflectance of changes in the sensor structure are investigated in detail and the principles for the design of the device are summarized in this paper. Results show that the device has a refractive index detection range of 1.33–1.49, with different sensing properties under TE and TM polarized light. This LMR sensor has a high sensitivity under TE polarized light with a sensitivity range of 83–420 °/RIU and a maximum quality factor of 9.9×105 RIU−1 under TM polarized light. We believe that the proposed structure can be broadly applied to chemical biomolecular detection, environmental monitoring, medical diagnosis, and other fields.