Using a spectral analysis of bright Chandra X-ray sources located in 27 nearby galaxies and maps of star-formation rate (SFR) and ISM surface densities for these galaxies, we constructed the intrinsic X-ray luminosity function (XLF) of luminous high-mass X-ray binaries (HMXBs), taking into account absorption effects and the diversity of HMXB spectra. The XLF per unit SFR can be described by a power law dN/d log L X,unabs ≈ 2.0(L X,unabs /10 39 erg s −1 ) −0.6 (M yr −1 ) −1 from L X,unabs = 10 38 to 10 40.5 erg s −1 , where L X,unabs is the unabsorbed luminosity at 0.25-8 keV. The intrinsic number of luminous HMXBs per unit SFR is a factor of ∼ 2.3 larger than the observed number reported before. The intrinsic XLF is composed of hard, soft and supersoft sources (defined here as those with the 0.25-2 keV to 0.25-8 keV flux ratio of < 0.6, 0.6-0.95 and > 0.95, respectively) in ∼ 2:1:1 proportion. We also constructed the intrinsic HMXB XLF in the soft X-ray band (0.25-2 keV). Here, the numbers of hard, soft and supersoft sources prove to be nearly equal. The cumulative present-day 0.25-2 keV emissivity of HMXBs with luminosities between 10 38 and 10 40.5 erg s −1 is ∼ 5×10 39 erg s −1 (M yr −1 ) −1 , which may be relevant for studying the X-ray preheating of the early Universe.