We propose an elliptical no-core optical fiber-based surface plasmon resonance (SPR) sensor to implement the simultaneous detection of temperature and refractive index (RI). The external surface of the elliptical fiber is coated with a gold film and then deposited with a polydimethylsiloxane (PDMS) layer as a temperature sensing medium. The excited plasmon mode can penetrate through the PDMS layer and then into the analyte, and therefore being sensitive to both changes of temperature and analyte RI. The elliptical structure can support $x$ - and $y$ -polarized resonance peaks which possess different characteristics of temperature and RI. By employing the dual-wavelength matrix method, the variations of the temperature and RI can be separated and detected simultaneously. Our numerical results show that the temperature coefficients of the two peaks are −4.492 nm/°C and −4.569 nm/°C, and the RI coefficients of them are 5709 nm/RIU and 5553 nm/RIU, respectively. Compared with the previous designs, the proposed design does not require the polishing and filling processes, and only has one simple external sensing channel. Therefore, it is expected to ease the difficulties in sensor fabrication and sensing operation.