There are many machining errors in the ultra-precision machining process that affect the surface-shape error of devices, so they also affect the optical performance. Manufacturers always evaluate machining accuracy based on surface form accuracy. But optical performance is the final evaluated index for the optical system, so it is insufficient to evaluate the effect of the machining error on the surface-shape error of only one mirror in machining process. The effect of machining error on optical performance needs further research. Analysis model of machining error influence is established based on the multi-body system theory and the optical ray tracing theory. The effect of the machining errors on the surface-shape error and the optical performance is researched. The main form of the surface-shape error in the system and its influences on modulation transfer function (MTF) are obtained. Then, the tolerance of the machining errors,main surface-shape error and angle error are obtained based on the requirements of optical performance. The main machining errors are found, which affect the optical performances of three-mirror system. The results provide a theoretical support to the control of the main machining errors and the realization of the performance-controllable manufacture for the off-axis three-mirror system.