Effective molecular representation learning is crucial for molecular property prediction and drug design. However, existing approaches struggle with limitations in insufficient annotations and suboptimal architecture design. For instance, Graph Neural Networks (GNNs) suffer from over-squashing, causing the loss of important structural details in molecules, thus impairing molecular representations. In this work, we propose a new class of GNNs, GNN-MolKAN and its augmented variant, GNN-MolKAN+, that integrate the Kolmogorov-Arnold Networks (KAN) architecture from AI + Science into GNNs to address these challenges. Additionally, we introduce Adaptive FastKAN (AdFastKAN), an advanced KAN that offers increased stability and speed, further enhancing the performance of standard GNNs. Notably, our approach holds three key benefits: 1) Superior Performance: GNN-MolKAN and GNN-MolKAN+ demonstrate superior prediction ability, robust generalization to unseen scaffolds, and versatile transferability across different GNN architectures. 2) Efficiency: These models require less computational time and fewer parameters while matching or surpassing the state-of-the-art (SOTA) self-supervised methods. 3) Few-shot Learning Ability: GNN-MolKAN demonstrates great potential in few-shot learning scenarios, achieving an average improvement of 6.97% across few-shot benchmarks. Overall, we validate our architecture on 6 classification datasets, 6 regression datasets, and 4 few-shot learning datasets, consistently achieving highly competitive results across all of them.