In this paper, first-principles calculations based on the density functional theory, are performed to investigate the effects of strain field on the electronic and magnetic properties of two-bilayer gallium nitride (GaN) nanosheets. The two-bilayer GaN nanosheet without surface modification forms a planar graphitic structure, whereas that with full hydrogenation for the surface Ga and N atoms adopts the energetically more favorable wurtzite structure. Surface hydrogenation is proven to be an effective way to induce a transition from indirect to direct band gap. The bare and fully-hydrogenated GaN nanosheets are nonmagnetic semiconductors. When only one-side Ga or N atoms on the surface are hydrogenated, the semihydrogenated two-bilayer GaN nanosheets will preserve their initial wurtzite structures. The two-bilayer GaN nanosheet with one-side N atoms hydrogenated transforms into a nonmagnetic metal, while that with one-side Ga atoms hydrogenated (H-GaN) is a ferromagnetic semiconductor with band gaps of 3.99 and 0.06 eV in the spin-up and spin-down states, respectively. We find that the two-bilayer H-GaN nanosheets will maintain ferromagnetic states under a strain field and the band gaps Eg in spin-up and spin-down states are a function of strain . As the tensile strain is +6%, the band gap in spin-up state reduces to 2.71 eV, and that in spin-down state increases to 0.41 eV for the two-bilayer H-GaN nanosheets. Under the compressive strain field, the two-bilayer H-GaN nanosheets will show a transition from semiconducting to half-metallici state under compression of -1%, where the spin-up state remains as a band gap insulator with band gap of 4.16 eV and the spin-down state is metallic. Then the two-bilayer H-GaN nanosheets will turn into fully-metallic properties with bands crossing the Fermi level in the spin-up and spin-down states under a compressive strain of -6%. Moreover, the value of binding energy Eb for the two-bilayer H-GaN nanosheet decreases (increases) monotonically with increasing compressive (tensile) strain. It is found that although hydrogenation on one-side Ga atoms of the two-bilayer H-GaN nanosheets is preferred to be under compressive strain, the two-bilayer H-GaN nanosheets are still the energetically favorable structures. The physical mechanisms of strain field tuning band gaps in the spin-up and spin-down states for the two-bilayer H-GaN nanosheets are mainly induced by the combined effects of through-bond and p-p direct interactions. Our results demonstrate that the predicted diverse and tunable electronic and magnetic properties may lead to the potential application of GaN nanosheets in novel electronic and spintronic nanodevices.