Bitcoin transactions include unspent transaction outputs (UTXOs) as their inputs and generate one or more newly owned UTXOs at specified addresses. Each UTXO can only be used as an input in a transaction once, and using it in two or more different transactions is referred to as a double-spending attack. Ultimately, due to the characteristics of the Bitcoin protocol, double-spending is impossible. However, problems may arise when a transaction is considered final even though its finality has not been fully guaranteed in order to achieve fast payment. In this paper, we propose an approach to detecting Bitcoin double-spending attacks using a graph neural network (GNN). This model predicts whether all nodes in the network contain a given payment transaction in their own memory pool (mempool) using information only obtained from some observer nodes in the network. Our experiment shows that the proposed model can detect double-spending with an accuracy of at least 0.95 when more than about 1% of the entire nodes in the network are observer nodes.