Two independent versions of the RNG based k-ε turbulence model in conjunction with the law of the wall have been applied to the numerical simulation of an axisymmetric turbulent impinging jet flow field. The two model predictions are compared with those of the standard k-ε model and with the experimental data measured by LDV (Laser Doppler Velocimetry). It shows that the original version of the RNG k-ε model with the choice of Cε1=1.063 can not yield good results, among them the predicted turbulent kinetic energy profiles in the vicinity of the stagnation region are even worse than those predicted by the standard k-ε model. However, the new version of RNG k-ε model behaves well. This is mainly due to the corrections to the constants Cε1 and Cε2 along with a modification of the production term to account for non-equilibrium strain rates in the flow.