  We present the latest results of a semi-analytic model of galaxy formation,
"New Numerical Galaxy Catalogue", which is combined with large cosmological
N-body simulations. This model can reproduce statistical properties of galaxies
at z < 6.0. We focus on the properties of active galactic nuclei (AGNs) and
supermassive black holes, especially on the accretion timescale onto black
holes. We find that the number density of AGNs at z < 1.5 and at hard X-ray
luminosity 10^{ 44 }< erg/s is underestimated compared with recent
observational estimates when we assume the exponentially decreasing accretion
rate and the accretion timescale which is proportional to the dynamical time of
the host halo or the bulge, as is often assumed in semi-analytic models. We
show that to solve this discrepancy, the accretion timescale of such less
luminous AGNs instead should be a function of the black hole mass and the
accreted gas mass. This timescale can be obtained from a phenomenological
modelling of the gas angular momentum loss in the circumnuclear torus and/or
the accretion disc. Such models predict a longer accretion timescale for less
luminous AGNs at z < 1.0 than bright QSOs whose accretion timescale would be
10^{ 7-8 } yr. With this newly introduced accretion timescale, our model can
explain the observed luminosity functions of AGNs at z < 6.0.
