A surface plasmon-based hexagonal photonic crystal fiber sensor is numerically computed and studied covering a large span of analyte refractive index from 1.33 to 1.40. Structural design parameters are optimized to improve the sensor performance. Investigation of sensor sensitivity has been performed by analyzing the electromagnetic behavior of light using finite element method-based mode solver. The studied sensor yields the maximum amplitude sensitivity of 3958.84  RIU^−  1 at analyte RI of 1.39 and moderate wavelength sensitivity of 8000  nm RIU^−  1 at analyte RI of 1.40. The observed results are also presented by changing the gold layer thickness, lattice period, and air hole diameter. The reported plasmonic sensor is an appealing aspirant in the field of biochemical sensing, biomolecule detection, and biological sample recognition.