Nowadays, computer networks have always been complicated deployment for both the scientific and industry groups as they attempt to comprehend and analyze network performance as well as design efficient procedures for their operation. In software-defined networking (SDN), predicting latency (delay) is essential for enhancing performance, power consumption and resource utilization in meeting its significant latency requirements. In this thesis, we present a graph-based formulation of Abilene Network and other topologies and apply a Graph Neural Network (GNN)-based model, Spatial-Temporal Graph Convolutional Network (STGCN), to predict end-to-end packet delay on this formulation. The evaluation uses STGCN to compare with other machine learning methods: Multiple Linear Regression (MLR), Extreme Gradient Boosting (XGBOOST), Random Forest (RF), and Neural Network (NN). Datasets in use include Abilene, 15-node scale-free, 24-node GEANT2, and 50-node networks. Notably, our GNN-based methodology can achieve 97.0%, 95.9%, 96.1%, and 63.1% less root mean square error (RMSE) in the most complex network situation than the baseline predictor, MLR, XGBOOST and RF, respectively. All the experiments show that STGCN has good prediction performance with small and stable prediction errors. This thesis illustrates the feasibility and benefits of a GNN approach in predicting end-to-end delay in software-defined networks.