Groundwater contamination due to municipal landfill sites is a threat to ground water integrity. This current research characterised the heavy metals in leachate from Soluos dumpsite in Lagos, Nigeria and assessed the groundwater quality at different distances from the dumpsite for both dry and wet seasons. The contaminants examined are lead, zinc, copper, nickel, chromium, iron, manganese, magnesium, calcium, sodium, potassium and chloride. The results showed that the concentration level of contaminants examined in groundwater samples in all the well investigated fall within the maximum acceptable concentration stipulated by World Health Organisation and National Agency for Food and Drug Administration and Control except for GW2 for wet season; but it will be higher than the level stipulated by the regulatory bodies in future based on the predicted values, hence there is a need to upgrade the dumpsite to prevent future contamination of groundwater. A predictive model for transport of contaminants through a porous medium used in this work predicted the contaminants concentration in groundwater samples near the dumpsite to a very appreciable level of above 93% confidence level, using finite difference method implemented in Matlab 7.0. This showed that the model parameters used which were obtained by sensitivity analysis of previous work of Jhamnani and Singh are suitable for Soluos dumpsite in Lagos State. Descriptive statistics such as mean, variation, standard deviation, standard error and coefficient of variance were used to describe the basic features of the results of groundwater samples.