In recent years, deep learning has received an excellent performance in the tasks of image feature extraction and image classification. Besides, the coding-based methods have been widely focused on because of their outstanding local description. In this paper, we propose a novel method for finger-vein recognition, which combines local coding and convolution neural network (LC-CNN). Based on local graph structure (LGS), a weighted symmetrical LGS is firstly proposed to locally represent the gradient relationship among the surrounding pixels. Then, the traditional local coding methods are reconstructed with a set of fixed sparse predefined binary convolution filters. To address the over-fitting of the network, we use the local coding convolution to alter standard convolution in pre-trained CNN. Finally, the extracted feature vector are input into a support vector machine (SVM) for images classification. Experimental results show that the proposed approach achieves better performance than the traditional coding methods on finger vein recognition.