The frequency response functions, and modal parameters are the premise for analyzing robot vibrations during robotic milling process, and modal parameters have strong posture-dependence. The finite element method and dynamic model often lose accuracy due to the difficulty in exactly modeling the stiffness and damping properties of robots. To predict the modal parameters quickly and accurately in all robot postures within the machining space, this paper proposes a modal parameter prediction method based on Gaussian process regression. The influence of joint angles and Euler angles of a six degree-of-freedom serial robot on the modal parameters of the robotic milling system is investigated. Based on this, a posture-related modal parameters prediction model is established to characterize the relationship between modal parameters and robot postures through 245 sets of modal testing experiments in the machining plane. The model can predict the posture-related modal parameters for all robot postures by a limited number of modal testing experiments. The proposed method is validated by experiments.