Despite their wide application across various fields, current molecular property prediction models struggle with the challenge of activity cliff, which refers to the situation where molecules with similar chemical structures display remarkable different properties. This phenomenon hinders existing models' ability to learn distinctive representations for molecules with similar chemical structures, and results in inaccurate predictions on molecules with activity cliff. To address this limitation, we first present empirical evidence demonstrating the ineffectiveness of standard training pipelines on molecules with activity cliff. We propose a novel approach that reformulates molecular property prediction as a node classification problem, introducing two innovative tasks at both the node and edge levels to improve learning outcomes for these challenging molecules with activity cliff. Our method is versatile, allowing seamless integration with a variety of base models, whether pre-trained or randomly initialized. Extensive evaluation across different molecular property prediction datasets validate the effectiveness of our approach.