The parameters of non-linear Muskingum model (NLMM) are usually assumed to be constant during the flood routing period. Recently, the need to consider a variable exponent parameter for the NLMM has been emphasised. A suitable continuous variable exponent parameter can substantially improve the model. In this study, an appropriate continuous inflow-based exponent is proposed for the NLMM. The discharges of inflow hydrographs of future events may be different and larger than the discharges of inflow hydrographs used in the calibration stage, and thus the proposed inflow-based function for the exponent parameter is considered such that it varies only in a small range regardless of the size of the future inflow hydrographs and their durations (safe extrapolation). When volumes of the inflow and outflow hydrographs are different, the lateral flows are expected to play a relevant role in the flood routing procedure. These effects are also considered in this research. The proposed model was implemented and tested on three different sets of benchmark hydrographs from the literature and the improvement in performance of the proposed model was considerable.