In this paper, a hollow-core negative curvature fiber (HC-NCF) with high birefringence is proposed for low refractive index (RI) sensing based on surface plasmon resonance effect. In the design, the cladding region of the HC-NCF is composed of only one ring of eight silica tubes, and two of them are selectively filled with the gold wires. The influences of the gold wires-filled HC-NCF structure parameters on the propagation characteristic are investigated by the finite element method. Moreover, the sensing performances in the low RI range of 1.20–1.34 are evaluated by the traditional confinement loss method and novel birefringence analysis method, respectively. The simulation results show that for the confinement loss method, the obtained maximum sensitivity, resolution, and figure of merit of the gold wires-filled HC-NCF-based sensor are −5700 nm/RIU, 2.63 × 10−5 RIU, and 317 RIU−1, respectively. For the birefringence analysis method, the obtained maximum sensitivity, resolution, and birefringence of the gold wires-filled HC-NCF-based sensor are −6100 nm/RIU, 2.56 × 10−5 RIU, and 1.72 × 10−3, respectively. It is believed that the proposed gold wires-filled HC-NCF-based low RI sensor has important applications in the fields of biochemistry and medicine.