Machine unlearning is a process of removing the impact of some training data from the machine learning (ML) models upon re- ceiving removal requests. While straightforward and legitimate, retraining the ML model from scratch incurs a high computational overhead. To address this issue, a number of approximate algorithms have been proposed in the domain of image and text data, among which SISA is the state-of-the-art solution. It randomly partitions the training set into multiple shards and trains a constituent model for each shard. However, directly applying SISA to the graph data can severely damage the graph structural information, and thereby the resulting ML model utility. In this paper, we propose GraphEraser, a novel machine unlearning framework tailored to graph data. Its contributions include two novel graph partition algorithms and a learning-based aggregation method. We conduct extensive experiments on five real-world graph datasets to illustrate the unlearning efficiency and model utility of GraphEraser. It achieves 2.06× (small dataset) to 35.94× (large dataset) unlearning time improvement. On the other hand, GraphEraser achieves up to 62.5% higher F1 score and our proposed learning-based aggregation method achieves up to 112% higher F1 score.