One of the primary challenges in wireless blockchain networks is to ensure security and high throughput with constrained communication and energy resources. In this paper, with curve fitting on the collected blockchain performance dataset, we explore the impact of the data transmission rate configuration on the wireless blockchain system under different network topologies, and give the blockchain a utility function which balances the throughput, energy efficiency, and stale rate. For efficient blockchain network deployment, we propose a novel Graph Convolutional Neural Network (GCN)-based approach to quickly and accurately determine the optimal data transmission rate. The experimental results demonstrate that the average relative deviation between the blockchain utility obtained by our GCN-based method and the optimal utility is less than 0.21%.