Display omitted •Proposed a three-dimensional convolutional neural network (3D-CNN) for heterogeneous composite material homogenization.•Network trained on labeled data generation by numerical simulation.•Tested uncertainty quantification ability and transferability of the trained model.•Demonstrated effectiveness and efficiency for predicting effective material properties. Homogenization is a technique commonly used in multiscale computational science and engineering for predicting collective response of heterogeneous materials and extracting effective mechanical properties. In this paper, a three-dimensional deep convolutional neural network (3D-CNN) is proposed to predict the anisotropic effective material properties for representative volume elements (RVEs) with random inclusions. The high-fidelity dataset generated by a computational homogenization approach is used for training the 3D-CNN models. The inference results of the trained networks on unseen data indicate that the network is capable of capturing the microstructural features of RVEs and produces an accurate prediction of effective stiffness and Poisson’s ratio. The benefits of the 3D-CNN over conventional finite-element-based homogenization with regard to computational efficiency, uncertainty quantification and model’s transferability are discussed in sequence. We find the salient features of the 3D-CNN approach make it a potentially suitable alternative for facilitating material design with fast product design iteration and efficient uncertainty quantification.