In this study, we investigated the viscosity, squeeze-film damping, and a SiC-based capacitive micro-accelerometer in rarefied air. A specific expression for the effective viscosity coefficient of the air was derived, and when the air pressure drops from the standard atmospheric pressure, the viscosity of the air will decrease accordingly. Decreases in the air pressure and the viscosity of the air lead to the change in the squeeze-film air damping in the micro-accelerometer, and both the viscous damping force and the elastic damping force of the air film between the moving electrode plate and the fixed electrode plate will also decrease. The damping coefficient and relative damping ratio of the micro-accelerometer in rarefied air were calculated, which was also confirmed by simulations. The changes of the damping coefficient and the relative damping ratio of the system will directly affect the dynamic characteristics of the micro-accelerometer. When the air pressure in the working environment is below the standard atmospheric pressure, the micro-accelerometer will be in an underdamping state. With the decrease in the air pressure, the working bandwidth of the micro-accelerometer will decrease significantly, and the resonant phenomenon may appear. However, the decrease in the air pressure will not have a notable impact on the response time of the micro-accelerometer. Therefore, this work provides a theoretical basis for the study of the performance characteristics of a SiC-based capacitive accelerometer in rarefied air.