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A surface plasmon resonance sensor based on a dual-groove photonic crystal fiber (PCF) for refractive index (RI) sensing with ultra-wide measurement range and high sensitivity is designed and theoretically investigated. The upper and right grooves of the PCF as different sensing channels are coated with Au or Au-TiO2 compound film. The influence of the parameters on the sensing performance of the designed sensor are analyzed. Numerical results show that the maximum wavelength sensitivity (WS) of 6800 nm/RIU with a wavelength resolution of 1.47 × 10^-5 RIU and maximum amplitude sensitivity (AS) of 5440 RIU^-1 for the x polarization in the ultra-wide measurement range from 1.25 to 1.43 have been achieved. For y polarization, the proposed sensor has a maximum WS of 13200 nm/RIU and AS of 3465 RIU^-1 in the detection range from 1.39 to 1.43. The corresponding wavelength resolution is obtained about 7.58 × 10^-6 RIU. Moreover, the ultra-wide range and high sensitivity of the sensor can be flexibly adjusted by a polarization controller to meet different practical requirements. Therefore, the proposed sensor would be a suitable candidate for medical testing, bio-sensing and environmental monitoring.