A simulation of contaminant dispersion in a water reservoir has been done using 2-D finite difference method(FDM). The steady state velocity field of the reservoir was computed using stream function-vorticity formulation of Wavier-Stokes equation and continuity equation. Based on the computed steady state velocity field, the transient convective diffusion equation of the contaminant dispersion was computed. For the 1m$ imes$1m reservoir model with inlet and outlet attached, it was shown that the center of circulation located toward right. For the numerical values of v =0.01($ extrm{cm}^2$/s) and D=0.6($ extrm{cm}^2$/s) and the flow of 50($ extrm{cm}^3$/s ), it was determined that the outflow had to be shut down in 18 seconds to prevent from severe pollution. Also the required time was computed to be 6 seconds for the inflow of 100 ($ extrm{cm}^3$/s). The result of this study is considered, hopefully, to be useful for the design of the water reservoir systems that are the subjects to various contamination.