Abstract: In the study of Rayleigh-Bénard (RB) convection, it is usually assumed that sidewalls are adiabatic. However, this is not always the case in real heat exchangers. Consequently, the flow structures and heat transfer will be inevitably affected by non-adiabatic walls. The effect of the thermal conductivity of sidewalls on RB convection is investigated by two- and three-dimensional direct numerical simulations with the sidewall temperature being set to the mean of the top and bottom temperatures. The working fluid is water with the Prandtl number Pr = 5.3 and the aspect ratio Γ of the simulation box is fixed to Γ = 1. The results are further compared with those of traditional RB convection with adiabatic sidewalls. It is found that in a certain range of the Rayleigh number Ra, the Nusselt numbers Nu of the top and bottom plates are not equal, which is closely related to the flow structures. The global heat transport is higher for the isothermal sidewall case than that of the adiabatic sidewall case. This is because, in the former case, part of the heat can be transferred directly through sidewalls instead of being absorbed by the thermal boundary layer. For the isothermal sidewall case, the global Reynolds number is smaller than that of the adiabatic sidewall case due to lower turbulence insensity.