Industrial robots are widely used in the field of processing because of their many advantages, such as their high flexibility and wide processing range, but the chatter phenomenon limits their application. In this study, a chatter model for the robot milling of natural marble is established that analyzes the effect of the milling parameters and position. The chatter stability model is first established based on the zeroth-order approximation method, in which the robot milling system is simplified into a vibration system with two degrees of freedom. The milling force coefficients are determined by robot milling experiments, and the modal parameters of the robot milling system are identified based on the single-point excitation and pickup methods, which are essential for the establishment of the chatter stability model. Second, robot milling experiments are conducted to verify the established model, proving its high prediction accuracy. Finally, the effect of the milling parameters and position on the chatter stability of the robot milling system is discussed. These conclusions can be references for the robot milling of natural marble.