This article is intended to investigate the advection-diffusion process using a difference-scheme based Monte Carlo simulation approach. This is accomplished while walking randomly in the solution region, and then the solution is recorded at a point at a certain time at the end of each random walk (RW). Therefore, the advantage of this technique is to use a more realistic approach based on probability of solving the model equation defining the system. In order to accurately analyse environmental responses, the computed solutions are discussed in detail. The proposed technique has been found to be effective in capturing the behaviour of the more involved processes.