Multiple-relaxation-time model (MRT) has more advantages than the many others approaches in the lattice Boltzmann method (LBM). Three-dimensional double MRT model is proposed for the first time for fluid flow and heat transfer simulation. Three types of cubic natural convection problems are solved with proposed method at various Rayleigh numbers. Two opposite vertical walls on the left and right are kept at different temperatures for all three types, while the remained four walls are either adiabatic or have linear temperature variations. For the first two types of cubic natural convections that four walls are either adiabatic or vary linearly, the present results agreed very well with the benchmark solutions or experimental results in the literature. For the third type of cubic natural convection, the front and back surfaces has linearly variable temperature while the bottom and top surface are adiabatic. The results from the third type exhibited more general three-dimensional characters. (C) 2015 Elsevier Ltd. All rights reserved.