Solute transport in low-permeability media such as clay has not been studied carefully up to present, and we are often unclear what the proper governing law is for describing the transport process in such media. In this study, we composed and analyzed the breakthrough curve (BTC) data and the development of leaching in one-dimensional solute transport experiments in low-permeability homogeneous and saturated media at small scale, to identify key parameters controlling the transport process. Sodium chloride (NaCl) was chosen to be the tracer. A number of tracer tests were conducted to inspect the transport process under different conditions. The observed velocity-time behavior for different columns indicated the decline of soil permeability when switching from tracer introducing to tracer flushing. The modeling approaches considered were the Advection-Dispersion Equation (ADE), Two-Region Model (TRM), Continuous Time Random Walk (CTRW), and Fractional Advection-Dispersion Equation (FADE). It was found that all the models can fit the transport process very well; however, ADE and TRM were somewhat unable to characterize the transport behavior in leaching. The CTRW and FADE models were better in capturing the full evaluation of tracer-breakthrough curve and late-time tailing in leaching.