This paper introduces an intelligent machining system (IMS) using an adaptive-network-based fuzzy inference system (ANFIS) predictor and the particle swarm optimization (PSO) algorithm with a hybrid objective function. The proposed IMS provides suitable machining parameters for the users, to satisfy different machining requirements such as accuracy, surface smoothness, and speed. First, the key computer numerical control parameters are selected, and the actual trajectories under different machining parameters obtained by linear scales are collected. These data are analyzed to obtain the machining time, contouring error, and tracking error, corresponding to the speed, milling accuracy, and surface smoothness, respectively. Second, a data-driven approach using ANFIS is established to obtain the corresponding relationship model between the machining parameters and three aforementioned performance indices. Subsequently, to establish the IMS, we combine the trained ANFIS model and establish a hybrid objective function optimization problem solved by PSO algorithm according the specific requirement of the user. Finally, the performance and effectiveness of the proposed machining system is demonstrated by experimental practical machining.