Hydraulic jump is a type of rapid variable currents, which has surface turbulence and twisting of water from the beginning to the end, and is known as an energy-wasting phenomenon. In this research, the numerical simulation of hydraulic jump was done in the case of initial negative step of 3 and 6 cm, bed roughness of 2 cm and reverse slope of 1.5 and 3%. RNG and k-ε disturbance models were used in this research. Also, two types of uniform and non-uniform grids were used. According to the numerical modeling results, the RNG turbulence model calculated the turbulence of the flow field more accurately compared to the K-ε turbulence model. The statistical indices of NRMSE, R2 and d for the numerical simulation results of the water surface profile were obtained as 10.1, 0.993 and 0.994 respectively. Also, the values of these indices were calculated for the speed profile simulation results, respectively 16.36, 0.944 and 0.97. The error of the numerical model in calculating the values of the velocity profile was higher compared to the water level profile, which can be attributed to the severe flow turbulence and instantaneous velocity fluctuations in any vertical direction within the range of occurrence of hydraulic jump and intensification of air-water mixing. Comparison of the simulation results with the laboratory results of water surface profile, velocity profile, conjugate depth ratio, rolling length and hydraulic jump length and energy loss ratio shows the capability of the numerical model in the three-dimensional simulation of the free hydraulic jump flow field.