Most of the current neural network models in quantum chemistry (QC) exclude the molecular symmetry and separate the well-correlated real space (R space) and momenta space (K space) into two individuals, which lack the essential physics in molecular chemistry. In this work, by endorsing the molecular symmetry and elementals of group theory, we propose a comprehendible method to apply symmetry in the graph neural network (SY-GNN), which extends the property-predicting coverage to orbital symmetry for both ground and excited states. SY-GNN is an end-to-end model that can predict multiple properties in both K and R space within a single model, and it shows excellent performance in predicting both the absolute and relative R and K space quantities. Besides the numerical properties, SY-GNN can also predict orbital properties, providing the active regions of chemical reactions. We believe the symmetry-endorsed deep learning scheme covers the significant physics inside and is essential for the application of neural networks in QC and many other research fields in the future.