To address the issue of temperature cross-sensitivity in refractive index (RI) measurement, a fiber-optic surface plasmon resonance (SPR) sensor based on dual D-shaped no-core fiber (NCF) is proposed and designed. The sensor mainly consists of D-shaped NCF, Ag/Fe2O3 composite film, and polydimethylsiloxane (PDMS), where the silver and Fe2O3 are successively coated on both D-shaped surfaces of NCF to generate SPR and enhance the oxidation resistance. The layer of PDMS coated on one D-shaped surface acts as a tunable ambient medium sensing the temperature variation and affecting the transmission spectrum of the sensor. Since the surface plasmon waves are excited in the two D-shaped surfaces with different films, the two RI and temperature-dependent spectral resonance peaks with different wavelengths will be produced. Research results demonstrate that the two peaks’ wavelengths have different responses to the variations of ambient RI and temperature. In the RI range of 1.36–1.376 and temperature range of 10–100 °C, the RI and temperature sensitivities reach 5 000 nm/RIU and −0.546 nm/°C, respectively. With the sensitivity coefficient matrix, simultaneous measurement of RI and temperature can be realized, and the corresponding accuracy is superior to 0.4×10-5 RIU and 0.037 °C.