A novel stitching machining method for ion beam figuring of optical mirrors is presented in this paper. Problems that should be dealt with in the stitching process such as shaping principle,algorithm for dwell time calculation,parameter identification and compensation for positioning errors are discussed. Based on Computer Controlled Optical Surfacing(CCOS)principle,the finite field nonlinear model is deduced from the stitching shaping mechanism;with the superposition property in the model,a modified Richardson-Lucy iterative algorithm is presented to deconvolute the dwell time for the stitching process;the effect of the positioning errors and the removal rate on the machining accuracy and shape is modeled and then the identification and compensation algorithm for these parameters is proposed based on this model.With these studies,shaping theory and algorithm are constructed,and then the stitching process for ion beam figuring comes into being.Figuring experiments are made on planar samples;the process convergence ratio is 10,which is similar to that in full aperture figuring.Theo- retical and experimental studies indicate that the stitching theory and algorithm in the ion beam figuring process presented in this paper are a novel method for fabrication of precision mirrors with lower cost. A novel stitching machining method for ion beam figuring of optical mirrors is presented in this paper. Problems that should be dealt with in the stitching process such as shaping principle, algorithm for dwell time calculation, parameter identification and compensation for positioning errors are discussed. on Computer Controlled Optical Surfacing (CCOS) principle, the finite field nonlinear model is deduced from the stitching shaping mechanism; with the superposition property in the model, a modified Richardson-Lucy iterative algorithm is presented to deconvolute the dwell time for the stitching process; the effect of the positioning errors and the removal rate on the machining accuracy and shape is modeled and then the identification and compensation algorithm for these parameters is proposed based on this model. These theories, shaping theory and algorithm are constructed, and then the stitching process for ion beam figuring comes into being .Figuring experiments are made on planar sa the process convergence ratio is 10, which is similar to that in full aperture figuring. The-retical and experimental studies indicate that the stitching theory and algorithm in the ion beam figuring process presented in this paper are a novel method for fabrication of precision mirrors with lower cost.