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 \la 0.3 occur preferentially in big galaxies with stellar mass M _ { * } \ga 2 \times 10 ^ { 10 } M _ { \odot } and metallicities Z peaking at \sim 0.6 Z _ { \odot } . However , the host galaxy stellar mass distribution of heavy SBBH mergers ( M _ { \bullet \bullet } \ga 50 M _ { \odot } ) is bimodal with one peak at \sim 10 ^ { 9 } M _ { \odot } and the other peak at \sim 2 \times 10 ^ { 10 } M _ { \odot } . The contribution fraction from host galaxies with Z \la 0.2 Z _ { \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 \la 0.3 occur preferentially in even more massive galaxies with M _ { * } > 3 \times 10 ^ { 10 } M _ { \odot } and in galaxies with metallicities mostly \ga 0.2 Z _ { \odot } and peaking at Z \sim 0.6 Z _ { \odot } , due to later cosmic assembly and enrichment of their host galaxies . SBBH mergers at z \la 0.3 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 .