Nitrogen is emitted extensively by industrial companies, increasing nitrogen compounds such as ammonia, nitrate, and nitrite in soil and water as a result of nitrogen cycle reactions. Groundwater contamination with nitrates and nitrites impacts human health. Mathematical models can explain groundwater contamination with nitrates and nitrites. Hydraulic head model provides the hydraulic head of groundwater. Groundwater velocity model provided x- and y- direction vector in groundwater. Groundwater contamination distribution model provides nitrogen, nitrate and nitrite concentration. Finite difference techniques are approximate the models solution. Alternating direction explicit method was used to clarify hydraulic head model. Centered space explained groundwater velocity model. Forward time central space was used to predict groundwater transportation of contamination models. We simulate different circumstances to explain the pollution in leachate water underground, paying attention to the toxic nitrogen, ammonia, nitrate, nitrite blended in the water.