In the era of the mass customisation, rapid and accurate estimation of the manufacturing cost of different parts can improve the competitiveness of a product. Owing to the ever-changing functions, complex structure, and unusual complex processing links of the parts, the regression-model cost estimation method has difficulty establishing a complex mapping relationship in manufacturing. As a newly emerging technology, deep-learning methods have the ability to learn complex mapping relationships and high-level data features from a large number of data automatically. In this paper, two-dimensional (2D) and three-dimensional (3D) convolutional neural network (CNN) training images and voxel data methods for a cost estimation of a manufacturing process are proposed. Furthermore, the effects of different voxel resolutions, fine-tuning methods, and data volumes of the training CNN are investigated. It was found that compared to 2D CNN, 3D CNN exhibits excellent performance regarding the regression problem of a cost estimation and achieves a high application value.