Graph neural network(GNN) has become one of the research field in the new wave of technological revolution and industrial transformation. High-performance GNN makes full use of structural information, aggregates neighbor information through a message passing mechanism, and finally successfully updates node embeddings, which effectively overcomes the limitations of traditional neural networks. However, in practice, an adversary can use the embedding of nodes to infer information about the architecture and parameters of the GNN model, which poses a potential threat to privacy. To solve this problem, we propose a privacy-preserving vertical federated graph neural network model training framework based on split learning (SVFGNN), an efficient secure gradient computation framework for vertical federated graph neural network models, which can be extended to existing GNN models. Specifically, in the forward propagation process, in order to reduce the client to perform a large number of calculation locally, we employ split learning for device-cloud collaborative training, and apply function-hiding multi-input function encryption technology to protect the parameters uploaded during model training. This solution not only ensures the security of model data and user privacy, but also creates high-precision models and supports lossless training. At the same time, in the process of backward propagation, in order to accurately predict the classification problem of nodes, we need to safely transmit errors and respond to client requests in a timely manner. To achieve this goal, we adopt hybrid encryption technology to realize cloud ciphertext data sharing, which eliminates point-to-point communication between various parties and significantly reduces communication overhead during model training. Compared to state-of-the-art works, our communication overhead scales linearly with the number of clients. Through the optimization of this research, we can better deal with the risk of privacy leakage, and provide a feasible security guarantee for the practical application of vertical federated graph neural network, and promote the development and progress of this field.