The temperature of the environment directly affects the accuracy of refractive index (RI) measurement. Therefore, we propose a double-sided polished surface plasmon resonance (SPR) RI fiber sensor, which is available for simultaneous measurement of the RI and temperature in real time. The proposed sensor uses single-mode fiber as a special double-sided polishing structure. The double-sided polishing regions are coated with a gold-silver hybrid film; one side is additionally coated with graphene layers to increase detection sensitivity, and the other side is coated with polydimethylsiloxane on the metal layer for temperature sensing. The simulation result shows that in the range from 1.33 to 1.35, RI sensitivity reaches as high as 2600 nm/RIU. In the range from 15°C to 85°C, temperature sensitivity reaches as high as -3.5n m/∘ C. The full width at half maximum is 65 nm. Compared with previous studies, the sensitivity is slightly improved, and an excellent temperature compensation effect can be achieved. It is suitable for high-precision measurement of the environment and biochemical aspects.