In order to understand the characteristics of Rayleigh-Benard convection of cold water near its density maximum in a rectangular cavity with an aspect ratio of 2, a series of direct numerical simulations are performed by using the finite volume method. The flow patterns and their evolution and heat transfer abilities are discussed in detail. Results indicate that the density maximum phenomenon affects significantly the R-B convection of cold water in a rectangular cavity. Compared with the cubical cavity, the critical Rayleigh number for the onset of convection in a rectangular cavity is small, and the effect of the aspect ratio on the critical value decreases with the increase of the density inversion parameter. Some new multiple-roll flow patterns are observed in the rectangular cavity. Furthermore, the distribution of the local Nusselt number depends on the flow pattern. Compared with the results in a cubical cavity, the overall heat transfer ability in the rectangular cavity is enhanced under the same control parameters. (C) 2016 Elsevier Ltd. All rights reserved.