Terahertz surface plasmon resonance (SPR) sensors have been regarded as a promising technology in biomedicine due to their real-time, label-free, and ultrasensitive monitoring features. Different authors have suggested a lot of SPR sensors, including those based on 2D and 3D metamaterials, subwavelength gratings, graphene, and graphene nanotube, as well as others. However, one of the traditional approaches to realize high sensitivity SPR sensors based on metal diffraction gratings has been studied poorly in the terahertz frequency range. In this article, a linear metal rectangular diffraction grating with high aspect ratio is studied. The influence of the grating structure parameters on the sensor sensitivity is simulated. Effects arising from different ratios of depth and width were discovered and explained. The results show that the sensitivity can be increased to 2.26 THz/RIU when the refractive index range of the gas to measure is between 1 and 1.002 with the resolution 5×10−5 RIU.