In this paper, a central-moments-based lattice Boltzmann method (CLBM) for incompressible thermal flows is proposed. In the method, the incompressible Navier-Stokes equations and the convection diffusion equation for the temperature field are solved separately by two different CLB equations. Through the Chapman-Enskog analysis, the macroscopic governing equations for incompressible thermal flows can be reproduced. The consistent forcing scheme (Fei and Luo, 2017) is adopted to incorporate forcing effect, and the implementation for CLBM is simplified by using simplified raw-moment sets. Compared with several D2Q5 multiple-relaxation-time(MRT) lattice Boltzmann methods for the temperature equation, the proposed method is shown to be better Galilean invariant through measuring the thermal diffusivities on a moving reference frame. Numerical simulations for several typical problems confirm the accuracy, efficiency, and stability of the present method. The grid convergence tests indicate that the proposed CLBM for incompressible thermal flows is of second-order accuracy in space. (C) 2017 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license.