Monitoring of the chatter vibration is necessarily required to do automatic manufacturing system. Therefore, we constructed a sensing system using tool dynamometer in order to monitor of chatter vibration on cutting process. Furthemore, an application of neural network using behavior of principal cutting force signals Is attempted. With the error back propagation trining process, the neural network memorized and classified the feature of principal cutting force signals. From obtained result, it is shown that the chatter vibration can be monitored effectively by neural network.