Abstract: Grinding chatter was a strong vibration between grinding wheel and workpiece, which reduced the surface quality of workpiece and accelerated grinding wheel wear. The key to solve the problem was improving the stability of grinding system. Firstly, the nonlinear dynamic model was established according to the dynamic macroscopic structure of cylindrical grinding, and the nonlinear dynamic equation was deduced, Faddeev algorithm was used to linearize the nonlinear dynamic equation to calculate the system characteristic values, and stability prediction was carried out to obtain the factors which affecting the system stability. Then, taking feed speed and grinding wheel length as an example, Matlab was used to draw the parametric stability chart with different values of each factor, and the time domain response chart and eigenvalue location chart corresponding to each parameter at the turning point of state change were studied, it was founded that the grinding process changed from unstable to stable when the feed speed increased from 10 mm/min to 12 mm/min, and the grinding process changed from stable to unstable when the length of the grinding wheel increased from 12 mm to 14 mm; parametric stability chart, time domain response chart and eigenvalue location chart were compared, and the conclusions obtained were consistent, which proves the correctness of the model finally.