The electronic and optical properties of the GaN monolayer hybrid with ZnO, MoS2 and MoSe2 are studied by means of density functional theory. The lattice mismatches of these three heterobilayers are less than 2.5% and they are stable with the binding energies larger than the ones of bilayer graphene. Despite of the indirect band gap of GaN monolayer, the three heterostructures exhibit direct band gap characteristics and their optical spectrums are broader than those of the isolated constituent layers because of interlayer coupling. Besides, both of biaxial tensile strain and external electric field (E-field) can effectively tune the band gaps of these heterostructures. The band gaps will decrease with the increase of tensile strain or the positive E-field strength while the ones will increase with the increase of the negative E-field intensity. Meanwhile, the adsorption edges of their imaginary parts of the dielectric function display corresponding redshift or blueshift characteristics and the band gaps may undergo direct to indirect transition beyond a critical strain or E-field intensity. The results shows that these GaN heterostructures can be good candidate materials for further investigations on the photo-related applications such as light-emitting diodes (LEDs), photodetection or solar energy conversion. (C) 2017 Elsevier B.V. All rights reserved.