To eliminate the interference of ambient temperature drift in the dynamic refractive index measurement, we propose a refractive index sensor based on a metamaterial structure with alternating grating and graphene. The effect of structure parameters on the response spectra is numerically simulated by the finite-difference time-domain method, the coupling mechanism is analyzed, and the designed structure is optimized. The research results indicate that this sensor with a composite structure possesses the dual spectral characteristics of multi-channel and ultra-narrow linewidth. In addition, the high absorption spectrum at near-infrared region is attributed to the coupling and excitation by F-P cavity resonance effect, magnetic polariton resonance effect, and destructive interference. Based on the differences in refractive index and temperature sensitivity under different resonance modes, with two resonant peak position wavelengths as information carrier and under the help of a matrix equation, the refractive index sensitivity reaches 358.6 nm/RIU after temperature compensation. The results show that the proposed sensor is effective in the real-time dynamic monitoring of samples in the wide refractive index range (1--1.6 RIU), and can avoid the influence of temperature drift, and thus it has more practicability.