In order to understand the effects of Rayleigh number and the density inversion parameter on the flow structures, the turbulent characteristics and the heat transfer ability, a series of large eddy simulations on turbulent Rayleigh-Benard convection in a cubical container with cold water near its maximum density were carried out. Results indicate that the large scale circulation (LSC) moves along the diagonal plane at small and medium density inversion parameters. However, at a large density inversion parameter, the LSC disappears. With the increase of the density inversion parameter, there are an increase of temperature in the bulk region and a decrease of penetration depth. Furthermore, with the increase of Rayleigh number, the deformation of isothermal surfaces becomes intense until the plumes are observed. At the same time, the scale of vortices reduces and the fluctuation of Nusselt number amplifies with the increase of Rayleigh number. Based on the numerical results, the dependence of Nusselt number on Rayleigh number and the density inversion parameter is achieved within a satisfactory uncertainty. (C) 2018 Elsevier Ltd. All rights reserved.