Autism Spectrum Disorder (ASD) is a complex neurodevelopmental disorder with a strong genetic component. This research work aims to identify key genes associated with ASD using a hybrid deep learning approach To identify influential/key genes associated with ASD, a protein-protein interaction (PPI) network is constructed, and a Graph Convolutional Network (GCN), a deep learning method, is employed. The GCN extracts features from the network structure based on gene interactions. Subsequently, Logistic Regression (LR) leverages these features to classify genes into influential and non-influential categories. The LR is chosen for its effectiveness in binary classification and ability to reveal feature importance, providing valuable insights into the underlying genetic mechanisms of ASD. Additionally, a simulation using the Susceptible-Infected (SI) model is conducted to calculate the infection ability of influential genes. This simulation demonstrates the higher infection ability of the genes identified by the proposed method, highlighting its effectiveness in pinpointing key genetic factors associated with ASD. Also, the result compared with existing centrality methods. The proposed method performs better to identify key genes involve in ASD. Our proposed method outperforms traditional measures in identifying key genes in the network, offering potential applications for identifying biomarkers. This innovative approach aligns with advancements in therapeutic and diagnostic systems, healthcare information systems, and neural engineering, providing a robust framework for future ASD research and potential applications in other neurodevelopmental disorders.