Motivated by the advances in 3D sensing technology and the spreading of low-cost robotic platforms, 3D object reconstruction has become a common task in many areas. Nevertheless, the selection of the optimal sensor pose that maximizes the reconstructed surface is a problem that remains open. It is known in the literature as the next-best-view planning problem. In this paper, we propose a novel next-best-view planning scheme based on supervised deep learning. The scheme contains an algorithm for automatic generation of datasets and an original three-dimensional convolutional neural network (3D-CNN) used to learn the next-best-view. Unlike previous work where the problem is addressed as a search, the trained 3D-CNN directly predicts the sensor pose. We present an experimental comparison of the proposed architecture against two alternative networks; we also compare it with state-of-the-art next-best-view methods in the reconstruction of several unknown objects. Our method is faster and reaches high coverage.