The accuracy of the circular grating is the key point for control precision of the single gimbal control moment gyroscope servo system used in civilian micro-agile satellites. Instead of using the multi reading heads to eliminate eccentricity errors, an algorithm compensation method based on a calibration experiment using a single reading head was proposed to realize a low-cost and high accuracy angular position measurement. Moreover, the traditional hardware compensation method using double reading heads was also developed for comparison. Firstly, the single gimbal control moment gyroscope system of satellites was introduced. Then, the errors caused by the installation of the reading head were studied and the mathematic models of these errors were developed. In order to construct the compensation function, a calibration experiment using the autocollimator and 24-sided prism was performed. Comparison of angle error compensation using the algorithm and hardware method was presented, and results showed that the algorithm compensation method proposed by this paper achieved the same accuracy level as the hardware method. Finally, the proposed method was further verified through a control system simulation.