A solar dish concentrator system has a large windward area and heavy structural mass, and under the action of wind loads and self-weight loads, foundation settlement can easily occur and cause the column (the azimuth axis) to tilt. Upon tilting, the azimuth axis is no longer perpendicular to the horizontal plane, causing a tracking error in the service of the solar dish concentrator system. In this paper, a tracking error model of a solar dish concentrator system is established based on the rigid body motion theory, which considers the azimuth axis tilt error. In this model, a radial angle and tangential angle parameters are used to describe the azimuth axis’s tilt angle and tilt direction. Under the tilt error of the azimuth axis, we analyze, in detail, the initial tracking position of a solar dish concentrator system, the system operation area, and the variation rule of tracking performance in long-term operation. The results show that under the azimuth axis tilt error of the solar dish concentrator system, the deviation of the initial tracking position of the solar dish concentrator system in the horizontal or vertical plane will reduce its tracking performance and the stability of tracking performance compared with the initial tracking position being due east. The tracking performance of a solar dish concentrator system and its stability are better in areas with a relatively low latitude. In different areas with close latitude, the tracking performance of the solar dish concentrator system and its stability are better, particularly with lower longitudes. During a whole year operation period, the tracking performance of an solar dish concentrator system in the first quarter and the fourth quarter is relatively better, and its stability in June and July is relatively better. This work can provide a theoretical basis for the installation, debugging, and error control of solar dish concentrator systems.