Abstract: Regarding the chatter problem during the milling process of bevel gear milling machines, a two-degree-of-freedom dynamic model is first established, integrating the forming principle of bevel gear milling and the mechanism of chatter. The dynamic cutting thickness and cutting forces during the milling process are then solved. Subsequently, system dynamic parameters are obtained through modal testing and calibration experiments. Following this, an improved full-discretization method for predicting milling stability is proposed, and system stability is determined based on Floquet theory. Simulation results demonstrate that the proposed method improves both convergence speed and computational accuracy compared to the zero-order semi-discretization method, first-order full-discretization method, and second-order full-discretization method. Finally, the stability lobe diagram of the milling system is derived using the improved full-discretization method. Experimental validation shows a high degree of agreement with the simulation results, indicating that the method can accurately predict milling stability and provide guidance for optimizing process parameters.