In this work, a surface plasmon resonance (SPR) sensor based on a novel liquid-core polymer optical fiber (POF) is proposed and numerically analyzed for refractive index (RI) detection. The polytetrafluoroethylene (PTFE) fiber is selected as the platform for SPR sensing. We combine the PTFE-based POF with the liquid-core structure by introducing a hole filled with analyte into the fiber center. The hole also acts as the fiber core to guide the incident light. This design helps to realize the detection of solutions with low RI values (around 1.33), while keeping the distinguished sensing characteristics of the liquid-core structure. Two side air holes are introduced into the cladding and a thin silver film protected by a titanium dioxide layer is plated on the wall of one air hole, which helps to control the mode coupling. In order to optimize the design of this sensor, the impacts of parameters such as metal layer thicknesses and the central hole radius are investigated using the full-vector finite element method (FEM). After optimization, our design shows a wavelength interrogation sensitivity reaching up to 16,750 nm/RIU and an average full-width at half-maximum (FWHM) of 42.86 nm in the RI range of 1.325–1.35.