In recent years, deep learning techniques have made significant advances in drug-target affinity (DTA) prediction. However, existing models still have considerable room for improvement in prediction accuracy, robustness, and generalization ability. To address these challenges, we present a novel hybrid model, MambaTransDTA, which integrates the Mamba architecture with the Transformer architecture to optimize drug-target interaction prediction. By combining Mamba's ability to capture long-range dependencies with the Transformer's modeling of local interactions, MambaTransDTA estimates drug-target affinity more comprehensively and achieves notable performance improvements. On the four benchmark data sets, MambaTransDTA demonstrates exceptional prediction accuracy, achieving mean squared error (MSE) values of 0.191 (Davis), 0.173 (KIBA), 0.302 (Metz) and 0.715 (BindingDB). These results represent a significant improvement over the next best existing model, with relative error reductions of 4.3% (Davis), 3.3% (KIBA), 4.7% (Metz) and 10.5% (BindingDB). Ablation experiments and analysis of different hybridization strategies confirm that the proposed MambaTransDTA architecture significantly improves prediction performance by fully leveraging the strengths of both architectures. Therefore, MambaTransDTA is poised to become an essential tool for AI-driven drug discovery. Our data and code are available at https://github.com/pdssunny/MambaTransDTA.