In this paper, a refractive index (RI) sensor is presented on the basis of the surface plasmon resonance (SPR) effect of double-ring hollow-core anti-resonant fiber (DR-HC-ARF), which has great sensitivity and wide detection range. In the design, the DR-HC-ARF consists of 12 silica tubes in two layers inside and outside, with the X-forward inner silica tube filled with gold wire. The simulation results indicated that the achievable maximum sensitivity, minimum resolution, and largest figure of merit of the DR-HC-ARF sensor filled with gold wire are -20600 nm/RIU, 4.85×10-6 RIU and 615.79 RIU-1, respectively, when measuring using the confinement loss approach. The maximum sensitivity, minimum resolution, and largest birefringence of the DR-HC-ARF sensor filled with gold wire are -21200 nm/RIU, 4.71×10-6 RIU and 2.38×10-4, respectively, for the birefringence analysis approach. The ultrahigh RI sensitivity of DR-HC-ARF sensor filled with gold wire paves a promising way on the applications in the field of biochemical detection.