Common terahertz wave sensors work under normal incidence conditions to distinguish the device under test (DUT). However, if the excited terahertz wave is not normal incident, its discrimination linearity will be affected. In this paper, a symmetrical gear-shaped terahertz metamaterial sensor is proposed. The structure of the sensor consists of a surface gear shaped metal pattern and a polyurethane substrate. This design has high transmittance in the range of 0.2~1.2 THz, and when the incident angle of electromagnetic waves changes within the range of 0°~70°, the resonance point of the sensor changes very stably and is insensitive to the incident angle, which compensates for the current shortcomings of sensors and has good ability to resist the uncertainty of the incident angle. At the same time, this sensing unit is also insensitive to the polarization of the incident wave, which expands the application range of terahertz sensors. The mathematical relationship between the sensitivity S and the refractive index of the object to be tested is derived. The sensitivity of the sensor is tested by the liquids with different refractive indices as the measurands. The result shows that there is a good linear relationship between the change of resonant frequency and the refractive index of sample. The sensitivity of the sensor is between -0.28 to -0.13 THz/RIU, demonstrating superior performance.