A high-sensitivity terahertz refractive index sensor controlled by the continuum bound state is designed in this paper. The sensor is composed of all-dielectric grating. By breaking the symmetry of the structure by translation, and the resonance can be transformed into a leakage mode resonance with a high quality factor (Q factor), and the extremely narrow linewidth cavity mode is very sensitive to the change of the refractive index of the surrounding medium. Using the finite element method, the transmission spectra with different asymmetry parameters, grating thickness, grating width, and refractive index of analytes are numerically simulated. The results show that the Q factor of the grating metasurface reaches 12620, the standard sensitivity is 31395 nm/RIU, and the FOM (Figure of merit) is 1000. The structure has potential applications in the field of highly sensitive photon sensors in the terahertz range.