Direct numerical simulations are performed for a fully developed horizontal turbulent channel flow under stable density stratification. The skin-friction and the Nusselt number agree well with the experimental results. Internal gravity waves (IGW) are found to be built up in the core region, where the turbulent heat flux is Suppressed drastically and the steep mean velocity and temperature gradients result. In the central region of the channel, the stable density stratification works as the virtual wall to block turbulent heat transfer. It is also found that the energy of IGW is transferred from the shear-induced turbulence through the pressure diffusion. With an increase in the stratification, the flow on one wall starts to become laminar, although it is still turbulent on the other.