Determining soil hydraulic properties in surface irrigation which the soil surface is used both to convey and infiltrate water is very important. It becomes an issue of great concern when fertilisers were also added to irrigation water during fertigation. The purpose of this study was to estimate infiltration, roughness and longitudinal dispersivity coefficients in conventional and alternate furrow fertigation using inverse modelling with a genetic algorithm. A surface fertigation model was used to simulate overland water flow and solute transport. To discover optimum values of the coefficients, a genetic algorithm with fifteen objective functions were used to minimise the differences between observed and simulated values of advance time, recession time, runoff hydrograph and runoff nitrate concentration. The results indicated that the infiltration, roughness and fertiliser dispersivity parameters were more sensitive to runoff, recession time and runoff nitrate concentration, respectively. The best simulations of advance and recession phases were obtained by the coefficients which were estimated from objective function that minimised the differences between observed and simulated values of advance and recession time, respectively. For improving simulation of runoff discharge, minimising the differences between observed and simulated values of runoff hydrograph as well as advance time was necessary. Similarly, the improved simulation of runoff nitrate concentration needed minimising differences between simulated and measured values of both advance and runoff nitrate concentration. The proposed inverse modelling approach with GA resulted in better performance as compared to the two-point method, particularly in fixed and variable alternate furrow fertigation.