A fiber/Ag-Cu films surface plasmon resonance (SPR) refractive index (RI) sensor composed of multimode fiber-no-core-fiber-multimode fiber (MMF-NCF-MMF) structure is designed. The sensing region length and Cu film deposition time of sensor are gradually optimized by the control variable method, which finally achieves the improvement of sensor properties. We experimentally compared the sensing performance of the fiber/Ag film and fiber/Ag-Cu films sensor. Experimental results show that the fiber/Ag-Cu films sensor has good linearity (R-square = 0.993), and its sensitivity is as high as 3957 nm/RIU in the refractive index detection range of 1.3328–1.3853, which is 1109 nm/RIU higher than the sensitivity of a conventional fiber/Ag film sensor. The sensor presented in this paper adopts the structure with composite metal film, which outperforms the common single-layer metal film in chemical stability such as oxidation resistance and mechanical hardness. Meanwhile, the SPR sensor with MMF-NCF-MMF structure has the advantages of convenient manufacture and compact structure. In conclusion, it can bestow a unique advantage in the field of biological detection or chemical analysis.