Chatter occurs frequently during the curve surface machining process, and it results in poor quality of finished surface. In order to identify chatter quickly and accurately, a method based on hidden Markov model (HMM) and support vector machine (SVM) for chatter recognition and prediction was proposed in this paper. Firstly, according to the phenomenon that the transition period of formation process of the curve surface machining chatter is short and difficult to distinguish from normal processing and chatter burst stages, a chatter identification and prediction system based on HMM–SVM hybrid model was designed, which combined the strong similarity classification ability of HMM and the strong classification ability of SVM. Then, the acceleration sensor was used to measure the tool vibration signal during the curve surface machining process, and the characteristic signals of machining states was obtained. Finally, HMM and HMM–SVM were used to carry out recognition experiments of curve surface machining state, and the results were analyzed and compared. The experimental results show that the proposed HMM–SVM method drastically improve the recognition accuracy rate, compared with HMM model alone. The recognition accuracies of the three processing states are over 95%, and the recognition time is less than 1.5s. Rapid identification and prediction of chatter are realized, which provide basis and guarantee for the subsequent chatter suppression.