Ion beam Figuring (IBF) of optical mirror is a polishing process based on CCOS with the application of ion sputtering effects. The material removal mechanism is in the atom scale, which can enhance the precision of the target surface to tens of nanometers. Without contact, this process can also promote the subsurface quality. In this paper, the Ion Beam Figuring Machine (IBFM) is introduced，which realizes the relative motion between the target surface and the ion source. Firstly, we describe the design method, the machine configuration and principal technical parameters. With the configuration and motion ability described, we introduce different scanning modes for surfaces of different scales respectively. Secondly presented is the precision analysis method for IBFM. Based on the CCOS principle, the relation between the convergence rate and positioning errors are deduced. This relation describes the precision requirement of machining process. Finally, the postposition algorithm of IBFM is analyzed. According to coordinate transition and rotation, the general transfer model for different scanning modes is given.