We report our investigations on the host galaxy properties of stellar binary black holes (SBBHs) by implementing simple recipes for SBBH formation and merger into cosmological galaxy formation model. If the time delay between SBBH formation and merger ranges from Gyr to the Hubble time, SBBH mergers at redshift z < 0.3 occur preferentially in big galaxies with stellar mass M* > 2 × 1010M⊙ and metallicities Z peaking around ~0.6Z⊙. However, the host galaxy stellar mass distribution of heavy SBBH mergers (with total black hole mass >50M⊙) is bimodal with one peak at ~109M⊙ and the other peak at ~2 × 1010M⊙. The contribution fraction from metal-poor host galaxies (Z < 0.2Z⊙) to heavy mergers is much larger than that to less heavy mergers. If SBBHs were formed in the early universe, their mergers detected at z < 0.3 occur preferentially in even more massive galaxies with M* > 3 × 1010M⊙ and in galaxies with metallicities mostly >0.2Z⊙ and peaking at Z ~ 0.6Z⊙.