Abstract The Muskingum model (MM) is widely used for flood routing due to its simplicity and low cost. In the Muskingum method, parameters are determined based on flood data measured by upstream and downstream hydrometric stations. During the next flood event, based on the hydrograph of the inflow to the river basin and the parameters of the Muskingum model of the previous flood, the hydrograph of the outflow from the basin is predicted. Therefore, the accuracy of the Muskingum model becomes important in flood forecasting. In this research, in addition to presenting a new nonlinear Muskingum model of the fifth type with lateral flow (NLMM5-L), the accuracy of different nonlinear Muskingum models for forecasting Daechung 2018 flood based on Daechung 2014 flood and its Muskingum model parameters is evaluated. The chimp meta-heuristic algorithm has been used to determine the parameters of different Muskingum models, which are defined as optimization problems. The value of the objective function for Wilson's case study in the NLMM5-L model is determined to be 1.34 (m3/s)2, which compared to previous research models, the NLMM5-L model performs very well. The number of decision variables in this model is 10. Different types of the Muskingum models i.e. NLMM1, NLMM2, NLMM3, NLMM4, NLMM5 and NLMM5-L are used for routing the Daechung 2014 flood and the value of the objective function for these models is determined to be 57.60, 56.76, 57.63, 54.75, 23.06 and 13.82(m3/s)2, respectively. The Daechung 2018 flood is predicted based on the parameters of the mentioned models. In the Daechung flood case study, it is found that the Muskingum model, which is more accurate in the parameter estimation and flood routing stage, is not necessarily more accurate in predicting the desired flood.