Modelling of contaminant transport in unsaturated soils is necessary to achieve an improved understanding of pollutant migration in the vadose zone, which differs significantly from that of fully saturated porous media. This paper deals with the application of a meshless method called Element Free Galerkin Method for modelling the contaminant transport through the unsaturated porous media with transient flow condition. A one dimensional advection-dispersion equation with linear retardation is considered. The unknown concentration values are approximated by using moving least square approximants, which are constructed by using a weight function, a linear basis function and a set of non-constant coefficients. The weak form of the governing equation is formulated and Lagrange multiplier method is used for enforcing the essential boundary condition. The van Genuchten model is used for describing the hydraulic properties of the soil. A numerical example is presented to illustrate the applicability of the proposed method and the results are compared with those obtained from the finite element method.