Genetic programming (GP) is recognized as a robust machine learning method for rainfall-runoff modelling. However, it may produce lagged forecasts if autocorrelation feature of runoff series is not taken carefully into account. To enhance timing accuracy of GP-based rainfall-runoff models, the paper proposes a new rainfall-runoff model that integrates season algorithm (SA) with multigene-GP (MGGP). The proposed SA-MGGP model was trained and validated for single- and two- and three-day ahead streamflow forecasts at Haldizen Catchment, Trabzon, Turkey. Timing and prediction accuracy of the proposed model were assessed in terms of different efficiency criteria. In addition, the efficiency results were compared to those of monolithic GP, MGGP, and SA-GP forecasting models developed in the present study as the benchmarks. The outcomes indicated that SA augments timing accuracy of GP-based models in the range 250% to 500%. It is also found that MGGP may identify underlying structure of the rainfall-runoff process slightly better than monolithic GP at the study catchment.