This study proposes a terahertz high-sensitivity sensor with a combined structure of double split-ring resonators and a metal strip as a basic unit. The destructive interference of the electromagnetic waves of the resonance rings and the metal strip with different radiation losses in far field makes the line width of the reflected resonance narrow, showing a typical asymmetric Fano-type reflection spectrum. Moreover, we verify that the quality factor of the tunable sensor can be tuned by changing the coupling distance between the double split-ring resonators and the metal strip through numerical simulations. When the coupling distance is 22 μm, the quality factor reaches 83. In addition, the sensitivity of the proposed metamaterial sensor to the analyte thickness is studied. The frequency shift exponentially increases as the thickness of the analyte increases and gradually saturates when the thickness exceeds 10 μm. Finally, we also investigate the impact of the analyte with different refractive indices on the proposed sensor. The proposed sensor exhibits extremely high refractive index sensitivity and the figure of merit, i.e., 171 GHz/RIU and 18.3, respectively, when the analyte thickness is 22 μm. This high-sensitivity sensor has extensive application prospects in biochemical detection.