The use of artificial intelligence to process sensor data and predict the dimensional accuracy of machined parts is of great interest to the manufacturing community and can facilitate the intelligent production of many key engineering components. In this study, we develop a predictive model of the dimensional accuracy for precision milling of thin-walled structural components. The aim is to classify three typical features of a structural component—squares, slots, and holes—into various categories based on their dimensional errors (i.e., “high precision,” “pass,” and “unqualified”). Two different types of classification schemes have been considered in this study: those that perform feature extraction by using the convolutional neural networks and those based on an explicit feature extraction procedure. The classification accuracy of the popular machine learning methods has been evaluated in comparison with the proposed deep learning model. Based on the experimental data collected during the milling experiments, the proposed model proved to be capable of predicting dimensional accuracy using cutting parameters (i.e., “static features”) and cutting-force data (i.e., “dynamic features”). The average classification accuracy obtained using the proposed deep learning model was 9.55% higher than the best machine learning algorithm considered in this paper. Moreover, the robustness of the hybrid model has been studied by considering the white Gaussian and coherent noises. Hence, the proposed hybrid model provides an efficient way of fusing different sources of process data and can be adopted for prediction of the machining quality in noisy environments.