A series of three-dimensional numerical simulations on Rayleigh-Benard convection of cold water near its density maximum in a cylindrical container of aspect ratio 2 were carried out by using the finite volume approach. The critical Rayleigh numbers for the onset of convection at different density inversion parameters were determined, and the stability ranges of all flow patterns were assured by increasing or decreasing the Rayleigh number. The heat transfer rates at different flow patterns were measured by the average Nusselt number on the hot wall. The results indicated that the critical Rayleigh number for the onset of the convection increases, the number of the flow patterns decreases and the transition between the flow patterns becomes simple with the increase of the density inversion parameter. There are some new flow patterns of Rayleigh-Benard convection of cold water, which do not appear for that of the common fluids. The flow patterns depend on not only the Rayleigh number and the density inversion parameter, but also the initial condition and the flow history. Furthermore, there is a hysteresis phenomenon during the transition of the flow pattern. (C) 2015 ElSevier Ltd. All rights reserved.