Terahertz (THz)-detection technology has been proven to be an effective and rapid non-destructive detection approach in biomedicine, quality control, and safety inspection, among other applications. However, the sensitivity of such a detection method is limited due to the insufficient power of the terahertz source and the low content, or ambiguous characteristics, of the analytes to be measured. Metamaterial (MM) is an artificial structure in which periodic sub-wavelength units are arranged in a regular manner, resulting in extraordinary characteristics beyond those possessed by natural materials. It is an effective method to improve the ability of terahertz spectroscopy detection by utilizing the metamaterial as a sensor. In this paper, a dual-band, high-sensitivity THz MM sensor based on the split metal stacking ring resonator (SMSRR) is proposed. The appliance exhibited two resonances at 0.97 and 2.88 THz in the range of 0.1 to 3 THz, realizing multi-point matching between the resonance frequency and the characteristic frequency of the analytes, which was able to improve the reliability and detection sensitivity of the system. The proposed sensor has good sensing performance at both resonant frequencies and can achieve highest sensitivities of 304 GHz/RIU and 912 GHz/RIU with an appropriate thickness of the analyte. Meanwhile, the advantage of multi-point matching of the proposed sensor has been validated by distinguishing four edible oils based on their different refractive indices and demonstrating that the characteristics obtained in different resonant frequency bands are consistent. This work serves as a foundation for future research on band extension and multi-point feature matching in terahertz detection, potentially paving the way for the development of high-sensitivity THz MM sensors.