We propose a dual-band terahertz metamaterial sensor (MS), which exhibits the low loss and high quality (Q) factor of electromagnetically induced transparency (EIT) effects at the frequencies of 0.89 THz and 1.56 THz simultaneously. The physical natures of EIT effects are analyzed by using numerical simulations and a “two particle” model. Further, THz sensing is performed based on the shifts of two EIT resonances when the analyte is coated at the metamaterial surface. The sensitivities of the sensor are investigated with respect to different thicknesses, cover areas and refractive indexes of the coated analyte film. Results show that the first EIT resonance is suitable for sensing the analyte with the refractive index from 1.5 to 2, while the second EIT resonance is more suitable for sensing the refractive index of the analyte from 1 to 1.5. The sensitivity is 280.8 GHz/RIU, the average Q value is 14.3, and the figure of merit (FOM) value is 4 for the first EIT resonance. Meanwhile, the sensitivity is 201.6 GHz/RIU, the average Q value is 56.9, and the FOM value is 11.5 for the second EIT resonance. Such a metamaterial sensor with high refractive index sensitivity and dual-band would have great potentials for promoting the developments of multi-band/broadband terahertz sensing and detection technology.