This present study has dealt with the natural convection of water in a rectangular vessel which has cooling point at the center of itself with numerically. The finite difference method (FDM) is presented for the two-dimensional computer simulation of water controlled by natural convection and heat conduction. According to this study, It is cleared that the overturn of density is clearly existed at the temperature of $4[^{circ}C]$ and that was compared with experimental result. Also the change of natural convection is known from the streamlines and isotherms. Most of all. It is cleared that the overturn of natural convection is changed with time caused by the fact that the temperature and density relationship of water.