This study derived an analytical solution of 1D convection-dispersion-linear dissipation equation with variable boundary using the Green’s function method, then compared the analytical solution with the numerical solution, and after that applied it to the heat conduction and solute transport experiments of a soil column. Results showed that the contributions of initial, upper and lower boundary conditions were independent. At the same time, analytical results matched the numerical simulation and the observed results of experiments well. As a conclusion, the analytical solution can represent the heat conduction and solute the transport processes well.