This paper introduces a hybrid filter bank-based convolutional network to develop a 3D face recognition system in different orientations. The filter banks approach has been mainly used for feature representation. The hybridization in filter banks is primarily generated by a fusion of principal component analysis (PCA) and independent component analysis (ICA) filters. Currently, the deep convolutional neural network (DCNN) has taken a significant step for improving the classification compared to other learning, though the feature learning mechanism of DCNN is not definite. We have used the cascaded linear convolutional network for 3D face classification using a composite filter-based network named PICANet. The networks consist of different layers: convolutional layer, nonlinear processing layer, pooling layer, and classification layer. The main advantage of these networks over DCNN is that the network structure is simple and computationally efficient. We have tested the proposed system on three accessible 3D face databases: Frav3D, GavabDB, and Casia3D. Considering different faces in Frav3D, GavabDB, and Casia3D, the system acquired 96.93%, 87.7%, and 89.21% recognition rates using the proposed hybrid network.