Person Re-Identification (ReID) requires comparing two images of person captured under different conditions. Existing work based on neural networks often computes the similarity of feature maps from one single convolutional layer. In this work, we propose an efficient, end-to-end fully convolutional Siamese network that computes the similarities at multiple levels. We demonstrate that multi-level similarity can improve the accuracy considerably using low-complexity network structures in ReID problem. Specifically, first, we use several convolutional layers to extract the features of two input images. Then, we propose Convolution Similarity Network to compute the similarity score maps for the inputs. We use spatial transformer networks (STNs) to determine spatial attention. We propose to apply efficient depth-wise convolution to compute the similarity. The proposed Convolution Similarity Networks can be inserted into different convolutional layers to extract visual similarities at different levels. Furthermore, we use an improved ranking loss to further improve the performance. Our work is the first to propose to compute visual similarities at low, middle and high levels for ReID. With extensive experiments and analysis, we demonstrate that our system, compact yet effective, can achieve competitive results with much smaller model size and computational complexity.