The geometric error modeling of NC machine tools is the key technique to dynamics design, precision analysis and error compensation. It is the important step to improve the precision of machine tools. A model of geometric errors for the machine tool based on multi-body system theory is found in this paper. The model is simple and it can not be affected by the structure of the NC machine tool. The error calculation, error compensation and command correction can be implemented by the geometric errors model. In the practical machining, the geometric errors educed by machine error model can be used to correct the ideal machining instructions, control the machine movement, so as to implement geometric error compensation and improve the machining accuracy.