This research article published by Global Journal of Pure and Applied Mathematics, Volume 16, Number 3, 2020This paper addresses the inverse source problem in a system of two-dimension advection-dispersion reaction equation with an emphasis on groundwater pollution source identification. We develop an inverse source problem method for identifying the unknown groundwater point sources utilizing only the boundary and interior measurements. We develop an identifiability criterion of the point sources from recording the oxygen deficit concentration relative to the biochemical oxygen demand concentration. We have also established an identification method that uses the records of oxygen deficit concentration and biochemical oxygen demand concentration to identify the source position as a solution to nonlinear dispersion current equations. We recover the source intensity function using the multi-dimension inverse Laplace transform of the de-convolution function without any need of an iterative process. The inverse Laplace transforms are approximated by shifted Legendre Polynomials. The results show that the proposed inverse problem method is accurate.