Groundwater solute transport phenomena typically occur in water-bearing zones with heterogeneous solute dispersive characteristics and/or media hydraulic properties. A radial basis function collocation method (RBFCM)-based numerical method was developed in order to investigate the ability of RBFCM to accurately portray solute transport phenomena under heterogeneous conditions. Simulations were performed for 1-D and 2-D transport scenarios in which scale-dependent dispersivity fields were taken into consideration and compared with available analytical solutions. Different radial basis functions (RBFs) were employed for assessing the sensitivity of the present method on the selected RBFs. The simulation results were also compared with the results of MT3DMS which is a modular three-dimensional transport model with alternative solution schemes including the method of characteristics, the implicit central finite difference and the third order total variation diminishing finite volume. The proposed model was also used to simulate a real case condition where solute transport through a two-layer soil medium had been investigated experimentally. The results showed that RBFCM represented a powerful tool for predicting the solute transport occurrence under heterogeneous conditions with high accuracy.