Today, the world major problem is the air pollution because of the rapid growth of industrial areas. The emission of pollutant by factories into the atmosphere is affecting human health and the environment, hence the need for accurate and efficient numerical schemes in modelling this problem is expedient. The purpose of this research is to compare the Finite Element methods (FEMs) and Finite Difference Methods (FDMs) for the simulation of air pollution problem and show the better numerical method out of the two methods. The C program and Matlab software were adopted for the efficient simulation, and result presentation of the two diffusion problem tested. The results show that both numerical models are efficient for solving the problem of diffusion and are suitable for air pollution emission control for a cleaner environment.