Abstract: In order to understand the special phenomena and laws of Rayleigh-Bénard convection of fluids with density extremum, a series of three-dimensional numerical simulations on Rayleigh-Bénard convection of cold water in a rectangular cavity when its horizontal walls were cooled and heated symmetrically relative to the temperature of the density extremum by using finite volume method is carried out. Flow structures and their bifurcation series are obtained, and the effects of the density extremum character, the Rayleigh number, the thermal boundary condition and the aspect ratio on Rayleigh-Bénard convection are discussed. The results demonstrate that the system of Rayleigh-Bénard convection of cold water with density extremum is much more stable than that of common fluid, and the flow structures and their bifurcation series are much more complex. Multiple flow patterns can coexist at a constant Rayleigh number and hysteresis phenomenon is observed in the flow evolution. The system loses its stability more easily and the heat transfer ability enhances with the increase of the aspect ratio. The system for conducting sidewalls is much more stable than that for insulating sidewalls and the heat transfer ability weakens. Furthermore, heat transfer correlations are proposed according to the multiple linear regression.