The impact of hydraulic conductivity on solute transport process in a highly heterogeneous aquifer was analyzed using the Monte-Carlo method. The logarithm of the hydraulic conductivity (lnK) of aquifer was considered as a non-stationary field with increments being a truncated fractional Lévy motion (fLm) generated using the SRA3DC code. MODFLOW and MT3DMS code were used to solve the flow and solute equations, respectively. Results indicate that larger C lead to a more heterogeneous hydraulic conductivity field. AsC increases, solute plumes show more significant anomaly with sharper leading edge and wider tailing edge. The solute plume extends and its second spatial moments increase as C increases, while the first spatial moments of the solute plume are independent of C values. The longitudinal macrodispersivity is scale-dependent and increases as a power law function of time. Increasing C results in an increase in longitudinal macrodispersivity. It was concluded that the nature of transport process is highly dependent on the heterogeneity of the hydraulic conductivity field.