With the extensive application of mass customization, fast and accurate responses to customer inquiries can not only improve the competitive advantage of an enterprise but also reduce the cost of parts at the design stage. Most cost estimation methods establish a regression relationship between features and cost based on the processing features of parts. Traditional methods, however, encounter certain problems in feature recognition, such as the inaccurate recognition of processing features and low efficiency. Deep-learning methods have the ability to automatically learn complex high-level data features from a large amount of data, which are studied to recognize processing features and estimate the cost of parts. First, this study proposes a novel three-dimensional (3D) convolutional neural network (CNN) part-feature recognition method to achieve highly accurate feature recognition. Furthermore, an innovative method of using the quantity to express the identified features and establishing the relationship between them and cost is proposed. Then, support vector machine and back propagation (BP) neural network methods are employed to establish a regression relationship between the quantity and cost. Finally, in comparison with the mean absolute percentage error values, the BP neural network yields a more accurate estimation, which has considerable application potential.