In this study, the numerical solution of the two-dimensional solute transport system in a homogeneous porous medium of finite length is obtained. The considered transport system has the terms accounting for advection, dispersion and first-order decay with first-type source boundary conditions. Initially, the aquifer is considered solute free, and a constant input concentration is considered at inlet boundary. The solution is describing the solute concentration in rectangular inflow region of the homogeneous porous media. The numerical solution is derived using a powerful method, viz. spectral collocation method. The numerical computation and graphical presentations exhibit that the method is effective and reliable during the solution of the physical model with complicated boundary conditions even in the presence of reaction term.