The cosmological evolution of the QSO luminosity functions (LFs) at NIR/optical/X-ray bands for 1.3 less than or similar to z less than or similar to 3.5 is discussed based on realistic QSO spectra. The accretion-disk theory predicts that although the QSO luminosities only depend on the mass-accretion rate, (M) over dot, the QSO spectra have dependence on the black-hole mass, M-BH, as well. The smaller is M-BH and/or the larger is (M) over dot, the harder does the QSO NIR/optical/UV spectrum become. We modeled the disk spectra which can reproduce these features, and calculated the LFs for a redshift of z similar to 3 with the assumption of new-born QSOs shining at the Eddington luminosity. The main results are: (i) the LFs observed at optical and X-ray bands can be simultaneously reproduced. (ii) LFs in the optical and X-ray bands are not sensitive to M-BH, while LFs at the NIR bands are; about a one order of magnitude difference is expected in the volume number densities at L-i,L-j similar to 10(46) erg s(-1) between the case that all QSOs would have the same spectral shape as that of M-BH = 10(9) M-circle dot and the case with M-BH = 10(11) M-circle dot. (iii) The resultant Us at NIR are dominated by 10(7) M-circle dot black holes at L-t,L-J less than or similar to 10(44) erg s(-1), and by 10(11) M-circle dot black holes at L-1,L-J greater than or similar to 10(46) erg s(-1). Future infrared observations from space (e.g. NGST) will probe the cosmological evolution of black-hole masses. For a redshift of z < 3, on the other hand, the observed optical/X-ray Us can be fitted if the initial QSO luminosity, L-0, is below the Eddington luminosity, L-Edd. Interestingly, the best-fitted values of l equivalent to L-0/L-Edd are different in the B- and X-ray bands; l(B) approximate to 2.5 l(x). The reason for this discrepancy is briefly discussed.