A new numerical model was doveloped to simulate density-dependent ground water flow and solute transport. Accuracy of a numerical model depends upon how well it simulates advection dominant situations because numerical oscillations can spoil solutions for these situations. Nonlinear oscillation-absorption finite element method. based on the variational principle, was employed. Unlike previous numerical models, this model can easily be expanded for more complex situations. Accuracy of the model is evaluated by comparing with analytical solutions and results of other numerical model.