The dual-permeability model (DPM) is highly efficient for describing bimodal transport in heterogeneous porous media. However, it uses only one domain to describe the matrix blocks, and it therefore ignores the impact of the mass transfer process inside the matrix blocks at the microscale. Therefore, in this study, to investigate the effect of the mass transfer process in dual-permeability media and the computational accuracy when considering it, the dual-permeability model with a transition domain (DPMTD) is proposed based on the DPM. Comparison of the DPMTD with the DPM by applying them to a sand column experiment with the same concept as the model reveals that the DPMTD captures the bimodal transport (especially the first peak) more effectively because it calculates the rapid exchange of solute in the early stage more accurately. Subsequently, the same conclusion is reached when both models are applied to a reported solute displacement experiment for an Andisol. In short, we suggest that the mass transfer process inside matrix blocks needs to be characterized in the model to achieve higher accuracy and provides a new approach for modeling the solute transport of preferential flow.