With the continuous expansion of communication network scale and the diversification of business demands, the traditional rule-based routing optimization methods have become difficult to meet the performance requirements in complex network environments. To address this issue, a multi-objective routing optimization method based on Graph Neural Network is proposed. This method abstracts the network topology into a graph structure and learns through the feature information of nodes and edges to achieve multi-objective (such as delay, throughput, and link load) optimized routing selection. To tackle the problems of traditional methods in handling dynamic network states and nonlinear constraints, a dynamic weight adaptive mechanism is introduced to enhance the adaptability of the routing strategy under different network states. By constructing network topologies of different scales in a simulation environment, the performance of the GNN routing optimization method is compared with that of Dijkstra algorithm, load balancing algorithm, and Q-learning algorithm. The experimental results show that the proposed method outperforms traditional algorithms in terms of average delay, throughput, and load balancing degree.