Compared with unimodal biometrics systems, multimodal systems can effectively improve the recognition performance in accuracy and security. However, exploring a robust feature representation approach suitable for multiple modalities remains a crucial and challenging problem in the personal authentication community. In this paper, we proposed a discriminant local coding based convolutional neural network (LC-CNN) for multimodal finger recognition by fusing fingerprint, finger-vein, and finger-knuckle-print traits. Specifically, for each tri-modal finger images, we first presented a weighted local gradient coding (WLGC) operator to enhance the discriminant characteristics and formed the local coding layer (LC-layer) by reconstructing the WLGC operator with a bank of predefined convolution layers. Then, we established a simple yet effective LC-CNN model to extract deeper tri-modal finger features. Finally, the extracted feature vectors of three modalities are concatenated and input into a Support Vector Machine (SVM) for image classification. Experimental results demonstrate that the proposed method achieves a stable, highly accurate, and robust performance in multimodal finger recognition.