With the development of blockchain technology, more and more attention has been paid to the intersection of blockchain and education, and various educational evaluation systems and E-learning systems are developed based on blockchain technology. Among them, Ethereum smart contract is favored by developers for its ``event-triggered" mechanism for building education intelligent trading systems and intelligent learning platforms. However, due to the immutability of blockchain, published smart contracts cannot be modified, so problematic contracts cannot be fixed by modifying the code in the educational blockchain. In recent years, security incidents due to smart contract vulnerabilities have caused huge property losses, so the detection of smart contract vulnerabilities in educational blockchain has become a great challenge. To solve this problem, this paper proposes a graph neural network (GNN) based vulnerability detection for smart contracts in educational blockchains. Firstly, the bytecodes are decompiled to get the opcode. Secondly, the basic blocks are divided, and the edges between the basic blocks according to the opcode execution logic are added. Then, the control flow graphs (CFG) are built. Finally, we designed a GNN-based model for vulnerability detection. The experimental results show that the proposed method is effective for the vulnerability detection of smart contracts. Compared with the traditional approaches, it can get good results with fewer layers of the GCN model, which shows that the contract bytecode and GCN model are efficient in vulnerability detection.