In this paper, we propose a novel Local Mesh High-order Pattern Descriptor (LMHPD) for face recognition. This description is constructed in a high-order derivative space and is integrated with a Convolutional Neural Network (CNN) architecture. Based on the information collected at a local neighborhood of reference pixel with diverse radiuses and mesh angles, a vectorized feature representation of the reference pixel is generated to provide micro-patterns. They are then converted to multi-channels to use in conjunction with the CNN. The CNN adopted in the proposed architecture is generic and very compact with a small number of convolutional layers. However, LMHPD is derived in such a way that it can work with most of the available CNN architectures. For keeping the computational cost and time complexity at the minimum, we propose a lighter approach of high-order texture descriptor with CNN architecture that can effectively extract discriminative face features. Extensive experiments on Extended Yale B and CMU-PIE datasets show that our method consistently outperforms several alternative descriptors for face recognition under various circumstances.