We have recently developed an efficient theoretical methodology that takes into account the weak nuclear quantum effect of hydrogen. In our methodology the differences between the weak hydrogen (nuclear) quantum effect and the Born-Oppenheimer approximation are described by a short-range Coulomb-like one-electron potential. Here, we focus on density functional theory (DFT) with the weak hydrogen quantum effect, and show that there is no strong DFT-functional dependence of the weak hydrogen quantum effect. In addition, we show an electron density analysis to investigate complex calculation results from different DFT functionals considering the hydrogen quantum effect. (C) 2011 Elsevier B.V. All rights reserved.