[Objective] To understand the scale-dependent dispersion and non-equilibrium kinetic adsorption etc. on solute transport in heterogeneous soils.[Methods] An analytical solution of one-dimensional reactive scale-dependent solute transport kinetic model was obtained by Laplace-transform and the inverse transform based on the complex formulation, and was illustrated to be accurate compared with the De Hoog numerical inversion method. Moreover, the distribution regularities of the solute concentration in soil were discussed and the scale effects of soil solute transport, sorption and degradation on the solute transport were analyzed by using the analytical solution.[Results] The calculations of the analytical solution and the De Hoog numerical inversion was in good agreement when inverse function Fourier series number N was 500. The solute concentration increased with the increase of the heterogeneity of soils and the decrease of adsorption and degradation of solute, and it had little change with the molecular diffusivity, first-order kinetic rate process and the degradation of the sorbed phase.[Conclusion] The research confirmed that the scale effects of soil solute transport, the sorption distribution between the two regions and the degradation in the liquid phase play major roles in solute transport through heterogeneous soils.