Graph Neural Networks (GNNs), particularly Graph Convolutional Networks (GCNs), have demonstrated strong performance across graph-learning tasks and are increasingly deployed via Machine Learning as a Service (MLaaS). Despite their success, existing GNN-based MLaaS platforms lack mechanisms to verify the integrity of inference procedures. Consequently, users cannot confirm whether the inference results they received are correct or not, nor can they verify if the results originate from the contracted model. We propose zkGCN, the first zero-knowledge proof-based integrity verification scheme for the GCN inference procedure. zkGCN enables verification of end-to-end inference integrity in MLaaS settings without exposing model parameters, ensuring that outputs originate from the legitimate model and computation trace. Our approach employs zk-SNARKs to construct proofs for the GCN inference process. We extract the computational logic of each hidden layer, express it as Rank-1 Constraint Satisfaction (R1CS), and design corresponding proof circuits. Experiments on three benchmark datasets for graph classification demonstrate the practicality and feasibility of zkGCN, with manageable overheads and succinct proof sizes.