Based on space meshing theory, the coordinate relation between the hob and the gear is established using the general tool which is used to product a standard involute gear. The space conversion matrix of hobbing movement is deduced. The movement controlling model of CNC gear-hobbing machine of the gear with arbitrary tooth profile is built. By taking cosine gear as an example, the modelling is studied. It provides a theoretical foundation for machining the arbitrary profile gear and the complex surface.