Floods are among the most important hydrological phenomena, and their accurate prediction plays a crucial role in water resources management and reducing flood-related damages. Despite their widespread application in flood routing, nonlinear Muskingum models still face challenges in accurately reproducing complex hydrographs, particularly multi-peaked hydrographs. This limitation is partly related to the fixed structure of the continuity equation and its inability to reflect temporal variations in the processes affecting flow storage. In this study, an Adaptive Nonlinear Muskingum Model (ANMM) was proposed, in which a time-dependent correction factor was incorporated into the continuity equation. This modification enables the temporal dynamics of storage and the effects of physical processes influencing flow routing, including infiltration, evaporation, temporary storage, lateral flows, and hydraulic inertia, to be considered. The Ecological Cycle Optimization (ECO) algorithm was employed to estimate the parameters of the proposed model. The performance of ANMM was evaluated using three case studies involving single-peaked and multi-peaked hydrographs. The results showed that, compared with the benchmark models, ANMM provided better performance in reproducing the routed hydrographs and achieved significant improvements in the SSQ, RMSE, MAE, and NSE indices. For the Linsley River, the reduction in SSQ error reached approximately 97%. In addition, the proposed model demonstrated a greater ability to reproduce peak discharge and the overall shape of the flood hydrograph. These findings indicate that incorporating temporal storage dynamics into the Muskingum model structure can improve the accuracy of flood routing, particularly for complex and multi-peaked hydrographs.