Graph Neural Networks (GNNs) have emerged as powerful machine learning models for numerous graph-based applications. However, existing GNN training frameworks cannot scale the training process elastically, resulting in poor training throughput and low cluster utilization. Although elastic training has been proposed for Deep Neural Networks (DNNs), it cannot be directly adopted to GNNs due to the prohibitive scaling cost and inefficient scheduling. In this paper, we present ElasGNN, an elastic GNN training framework that achieves efficient dynamic resource allocation for GNN jobs. ElasGNN proposes an efficient elastic training engine to achieve high-performant GNN job scaling and introduces novel graph repartitioning algorithms for both scale-in and scale-out processes to further minimize the scaling cost. Moreover, ElasGNN designs an efficient elastic scheduler, utilizing a scaling-cost-aware scheduling policy to improve the GPU utilization and system throughput. The experimental results show that the ElasGNN can achieve shorter job completion time and makespan for training jobs of diverse GNN models.