Surface plasmon resonance (SPR) optical fiber methane sensors provide promising routes for gas monitoring, yet most existing anti‐resonant hollow‐core fiber (ARHCF) SPR schemes lack multi‐parameter collaborative analysis and detailed polarization‐dependent mechanism interpretation. In this paper, we computationally investigate an SPR methane sensor based on inner‐gold‐coated ARHCF using the finite‐element method. Three critical structural parameters, including gold‐film thickness, methane‐sensitive cryptophane‐A film thickness, and anti‐resonant tube wall thickness, are comprehensively studied. The Y‐polarized FM exhibits higher confinement loss and stronger SPR coupling, while the X‐polarized mode delivers more stable sensing response against structural variation. As the gold‐film thickness increases from 30 nm to 37 nm, the SPR resonance wavelength shows a stable linear blue‐shift. A distinctive non‐monotonic spectral response accompanied by an abrupt wavelength jump is observed when adjusting sensitive‐film thickness within 2.5–3.5  μ m, and optimal sensing performance is obtained at 3.0 μ m sensitive‐film thickness. Tuning anti‐resonant tube thickness can effectively shift the SPR resonance wavelength, achieving maximum coupling strength at 0.30 μ m. Benefiting from the open hollow‐core architecture, the proposed sensor enables sufficient gas‐light interaction. This work clarifies parameter‐modulation mechanisms and offers feasible design references for ARHCF‐based SPR methane gas sensors.