With considering the distance-dependent diffusion coefficient, a one-dimensional contaminant diffusion model was developed. An analytical solution was obtained by using the orthogonal expansion method. The corresponding program was compiled on the basis of the proposed solution, and the effect of the relevant parameters on contaminant transport was analyzed. The results indicate that the diffusion coefficient has complex effects on the transport of contaminants. On one hand, the initial diffusion coefficient and heterogeneity parameter will affect the time of contaminant concentration reaches steady state, and on the other hand, the heterogeneity parameter affects the concentration of steady state. In addition, the influence of related parameters on the bottom flux of contaminant was discussed. The proposed analytical solution can be used for verification of complicated numerical models and experimental data fitting.