Graph Neural Networks (GNNs) have become a popular toolkit for generative floor plan design. Although design variation has improved greatly, few studies consider nongeometrical characteristics, such as building performance, in the generative design process. This paper presents a GNN-based approach to predict the energy performance for floor plan customization (energy-aware design). The approach lays the foundation for a performance-aware generative design using GNN. The results show that the GNN can achieve high accuracy in energy performance prediction.