We present results of near-infrared photometry (J, H, K_S) for a sample of active galactic nuclei (AGNs) obtained from hard X-ray surveys with ASCA. The sample covers the AGNs at z=0.1-1 with L(2-10keV)=10^42-10^46 erg/s with very high completeness. The fraction of red (J-K_S>2 mag) AGNs in our sample is 2(+-1)%, which is comparable to that for optically- or UV-selected quasi-stellar objects (QSOs, i.e. luminous AGNs). The number of red AGNs found in our sample is also consistent with that expected from the surface density of red AGNs found in 2MASS by Cutri et al. (2001). We find that the anomalously-small dust-to-gas ratios in circumnuclear gas, which is seen in some AGNs with Seyfert-class luminosity, also occur in the QSOs (AGNs with luminosity of L(2-10keV) > 10^44.5 erg/s). For all the QSOs with an X-ray absorption of N_H > 10^22 /cm2 in our sample, the values of A_V/N_H are smaller than the Galactic value by a factor of 5 to 100. Since a fraction of this population among the QSOs in our sample is about 30%, such fraction of optical/UV-selected type 1 QSOs known to date may show type 2 nature in X-ray.