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Milling chatter will not only cause chatter marks on the surface of the machined parts and reduce the surface quality of the machined parts, but also aggravate tool wear and reduce the life of the machine tool. According to the influence of the tool posture of the ball-end milling cutter affecting on the flutter generated during the machining process, the milling dynamics model under the influence of the tool posture was built. The milling dynamic model was solved by the third-order Newton-Hermite interpolation fully discrete method, and the state transition matrix of the system was obtained. The Floquet theory was used to judge the milling stability of the milling cutter under different tool postures, and the tool posture stability prediction map of the ball-end milling cutter was constructed. The experiment determines that the horizontal upward cutting method has the best stability and the lowest surface roughness of the workpiece, which could verify the validity of the stability prediction map. [ABSTRACT FROM AUTHOR]