In this paper, we propose a new architecture of 3D deep neural network called 3D Hahn Moments Convolutional Neural Network (3D HMCNN) to enhance the classification accuracy and reduce the computational complexity of a 3D pattern recognition system. The proposed architecture is derived by combining the concepts of image Hahn moments and convolutional neural network (CNN), frequently utilized in pattern recognition applications. Indeed, the advantages of the moments concerning their global information coding mechanism even in lower orders, along with the high effectiveness of the CNN, are combined to make up the proposed robust network. The aim of this work is to investigate the classification capabilities of 3D HMCNN on small 3D datasets. The experiment simulations with 3D HMCNN have been performed on the articulated parts of McGill 3D shape Benchmark database and SHREC 2011 database. The obtained results show the significantly high performance in the classification rates of the proposed model and its ability to decrease the computational cost by training low number of features generated by the first 3D moments layer.