This paper proposes a novel design for a highly sensitive high-resolution localized surface plasmon resonance (LSPR) biochemical sensor. The geometrical structure of the sensor consists of three segments. The first segment comprises single-mode fibers located in the output and input ends of the sensor. The second and third segments comprise rectangular nanometal arrays and serve as the analyte regions of the sensor; the amount of displacement between these two segments is one rectangular nonmetal particle. We integrated two breakthrough methods, the object meshing method and the boundary meshing method, with the finite element method to effectively improve the accuracy of simulation outcomes and reduce the amount of time and memory required for performing calculations. Subsequently, we constructed the proposed LSPR biochemical sensor, and the results indicated that the proposed sensor exhibited excellent geometric structure and spectral characteristics. Specifically, the sensor is short (approximately 250 μm) and features high resolution (approximately −130 dB) and high sensitivity (approximately 126,849.1333 nm/RIU).