Flow in a concentric annular passage with a rotating inner cylinder, which is called Taylor-Couette flow, is important in industrial applications, such as electric motor which requires not only effective cooling of rotating shaft but also saving power required for the axis rotation. When the through flow is superposed, which is called Taylor-Couette-Poiseuille flow, it affects the cooling efficiency and the torque required for the axis rotation. To the authors' knowledge, previous studies have been focused on either the Nusselt number or the torque coefficient in the Taylor-Couette-Poiseuille flow. Therefore, it is difficult to estimate the through -flow effects on both of them under the same geometry and flow conditions. In this study, the through -flow effects on both the Nusselt number and the torque coefficient in the Taylor-Couette-Poiseuille flow under the same geometry and flow conditions were investigated by performing large eddy simulation. The through -flow Reynolds number, Re, was varied from 500 to 8000 under constant Taylor and Prandtl numbers of Ta=4000 and Pr=0.71, respectively. The Nusselt number and the torque coefficient had similar trend to each other with the increase of Re. They decreased by 25% for the change of Re from 0 to 1000 and were nearly constant for the change of Re from 4000 to 8000. Contribution of the advection, turbulent transport and diffusion terms to the Nusselt number and the torque coefficient were evaluated by using the equations proposed by the authors. The contribution of the advection term was nearly zero for Re from 500 to 8000, which was contrary to the case without through -flow (Re=0). As Re increased, the contribution of the turbulent transport term decreased but that of the diffusion term did not change so much. The friction factor in the axial direction varied as Re-0.75 of which power was between laminar (Re-1) and turbulent (Re-0.25) correlations in a smooth stationary pipe flow.