In this paper we are presenting a numerical model to simulate transient flow and solute transport through a variably saturated zone. The mixed form of the Richards equation is used for the solution of the flow component as it is mass conserving, and the advection dispersion equation (ADE) is used for the solute transport. The Richards equation is solved numerically by finite difference and modified Picards iteration is used to deal with its inherent nonlinearity, and the resulting matrix is solved by a strongly implicit procedure. The numerical solution of ADE poses oscillations when there is a sharp front due to discontinuity in the solution. In this paper, we are presenting a numerical scheme to address the problems faced by the advective dominant front. The ADE is solved by the operator split method in which advection is solved by explicit finite volume and dispersion by the fully implicit finite difference method. A new numerical scheme is presented for the solution of the advection part of the equation. The advection flux is solved by using a locally one-dimensional approach, with the predictor-corrector method for the time step. Each step is made total variation diminishing to avoid oscillations. Performance of the model is tested for a few cases, like flow and transport into very dry soils, transient unconfined recharge and drainage through seepage face, and transient infiltration into randomly heterogeneous soils. The model is also used to study the effect of water table boundary and seepage face on the movement of solute.