Nowadays, deep learning is widely applied to extract features for similarity computation in person re-identification (re-ID) and have achieved great success. However, due to the non-overlapping between training and testing IDs, the difference between the data used for model training and the testing data makes the performance of learned feature degraded during testing. Hence, re-ranking is proposed to mitigate this issue and various algorithms have been developed. However, most of existing re-ranking methods focus on replacing the Euclidean distance with sophisticated distance metrics, which are not friendly to downstream tasks and hard to be used for fast retrieval of massive data in real applications. In this work, we propose a graph-based re-ranking method to improve learned features while still keeping Euclidean distance as the similarity metric. Inspired by graph convolution networks, we develop an operator to propagate features over an appropriate graph. Since graph is the essential key for the propagation, two important criteria are considered for designing the graph, and three different graphs are explored accordingly. Furthermore, a simple yet effective method is proposed to generate a profile vector for each tracklet in videos, which helps extend our method to video re-ID. Extensive experiments on three benchmark data sets, e.g., Market-1501, Duke, and MARS, demonstrate the effectiveness of our proposed approach.