  Understanding the host galaxy properties of stellar binary black hole (SBBH)
mergers is important for revealing the origin of the SBBH gravitational-wave
sources detected by advanced LIGO and helpful for identifying their
electromagnetic counterparts. Here we present a comprehensive analysis of the
host galaxy properties of SBBHs by implementing semi-analytical recipes for
SBBH formation and merger into cosmological galaxy formation model. If the time
delay between SBBH formation and merger ranges from $\la$\,Gyr to the Hubble
time, SBBH mergers at redshift $z\la0.3$ occur preferentially in big galaxies
with stellar mass $M_*\ga2\times10^{10}\msun$ and metallicities $Z$ peaking at
$\sim0.6Z_\odot$. However, the host galaxy stellar mass distribution of heavy
SBBH mergers ($M_{\bullet\bullet}\ga50\msun$) is bimodal with one peak at
$\sim10^9\msun$ and the other peak at $\sim2\times10^{10}\msun$. The
contribution fraction from host galaxies with $Z\la0.2Z_\odot$ to heavy mergers
is much larger than that to less heavy mergers. If SBBHs were formed in the
early universe (e.g., $z>6$), their mergers detected at $z\la0.3$ occur
preferentially in even more massive galaxies with $M_*>3\times10^{10}\msun$ and
in galaxies with metallicities mostly $\ga0.2Z_\odot$ and peaking at
$Z\sim0.6Z_\odot$, due to later cosmic assembly and enrichment of their host
galaxies. SBBH mergers at $z\la0.3$ mainly occur in spiral galaxies, but the
fraction of SBBH mergers occur in elliptical galaxies can be significant if
those SBBHs were formed in the early universe; and about two thirds of those
mergers occur in the central galaxies of dark matter halos. We also present
results on the host galaxy properties of SBBH mergers at higher redshift.
