A new zero flux moving boundary conditions to solve the non-equilibrium single-component dispersion-advection transport problem containing NAPL have been introduced. The resultant model can overcome many approximations in the model which is done by previous study and give more precise analytical solution to the aqueous (or gas) phase concentration profile, NAPL saturation and the moving front speed. From the results, it is clear that the number of pore volumes (P), which are required for removing all NAPL under equilibrium conditions, plays a role in the differences between the two models' predictions. The NAPL saturation profile predicted by the two models is the same. At very low P the predicted value of the front speed by the present model is half of the value predicted by Brouwers and Augustijn model and increases gradually with P. It reaches 0.99 when P is 100.