Graph Neural Networks (GNN) has become a powerful graph data processing method, which has been widely used in node classification, link prediction, and other graph analysis tasks. Due to the diversity and complexity of graph structures and information propagation, as well as the handling of heterogeneous graphs, etc., the design of GNNs presents many challenges. The existing methods have high classification accuracy, but their structures are very complex. In this paper, a graph neural network architecture search framework named MO-GNN, which is based on multi-objective evolutionary algorithm is proposed. Furthermore, a weight sharing strategy MO-GNN-WS is proposed to reduce the resource consumption caused by weight training of different architectures. To verify the performance of the proposed algorithm, experiments on four popular graph datasets are used for transduction and induction tasks. The experimental results show that the MO-GNN-WS algorithm outperforms the most advanced neural network architecture search methods in terms of classification accuracy and resource consumption.