Chattering is one of the most important factors affecting productivity of robot machining. This paper investigates the pose-dependent cutting stability of a 5-DOF hybrid robot. By merging the complete robot structural dynamics with the cutting force at TCP, an effective approach for stability analysis of the robot milling process is proposed using the full-discretization technique. The proposed method enables the computational efficiency to be significantly improved because the system transition matrix can be simply generated using a sparse matrix multiplication. Both simulation and experimental results on a full size prototype machine show that the stability lobes are highly pose-dependent and primarily dominated by the lower-order structural modes.