A study of the electrical conductivity of mechanical mixture of both the carbon nanotubes (CNTs) (with work function of $\cong$ 4.7 eV) and the Cu and Al metal microparticles (with lower work functions of 4.2 and 4.0 eV, respectively) under compression is provided. As shown, the electrical conductivity of the Al and Cu powders is essentially increased with addition of the CNTs (up to 30 wt.%). The electrical conductivity dependence on the density of a powder mixture of Al with CNTs is characterized by a deep minimum observed at the concentration of 9.6 wt.% CNTs. This feature is a result of the electrons’ localization in the Al$_2$O$_3$ film formed on a sample surface. A number of factors, in particular, a shift of the Fermi level of the CNTs deep into the valence band, explain the sharp decrease in the electrical conductivity of the Al + CNTs composite, unlike the Cu-based composite.