The proteins within the human epidermal growth factor receptor (EGFR) family, members of the tyrosine kinase receptor family, play a pivotal role in the molecular mechanisms driving the development of various tumors. Tyrosine kinase inhibitors, key compounds in targeted therapy, encounter challenges in cancer treatment due to emerging drug resistance mutations. Consequently, machine learning has undergone significant evolution to address the challenges of cancer drug discovery related to EGFR family proteins. However, the application of deep learning in this area is hindered by inherent difficulties associated with small‐scale data, particularly the risk of overfitting. Moreover, the design of a model architecture that facilitates learning through multi‐task and transfer learning, coupled with appropriate molecular representation, poses substantial challenges. In this study, we introduce GraphEGFR, a deep learning regression model designed to enhance molecular representation and model architecture for predicting the bioactivity of inhibitors against both wild‐type and mutant EGFR family proteins. GraphEGFR integrates a graph attention mechanism for molecular graphs with deep and convolutional neural networks for molecular fingerprints. We observed that GraphEGFR models employing multi‐task and transfer learning strategies generally achieve predictive performance comparable to existing competitive methods. The integration of molecular graphs and fingerprints adeptly captures relationships between atoms and enables both global and local pattern recognition. We further validated potential multi‐targeted inhibitors for wild‐type and mutant HER1 kinases, exploring key amino acid residues through molecular dynamics simulations to understand molecular interactions. This predictive model offers a robust strategy that could significantly contribute to overcoming the challenges of developing deep learning models for drug discovery with limited data and exploring new frontiers in multi‐targeted kinase drug discovery for EGFR family proteins.