This study adopted density functional theory and the Hubbard-U method in an investigation of the electronic and optical properties of pure ZnO and Ga-doped ZnO. The difference in the lattice constant between calculated results and experimental measurements is less than 1%, while the calculated band gap of pure ZnO is in excellent agreement with experimental values. Three structures, including the substitution of Ga for Zn (Gas(Zn)), interstitial Ga in an octahedron (Gai(oct)), and interstitial Ga in a tetrahedron (Gai(tet)), were considered. Calculations related to formation energy revealed that Gas(Zn) forms more easily than Gai(oct) and Gai(tet). All three of the Ga defect models resulted in an upward shift in the Fermi level into the conduction band, resulting in n-type conductive characteristics and expansion of the optical band gap beyond that of pure ZnO. In the Gas(Zn) model, the average transmittance levels in the visible and UV regions were 90.5% and 77.8%, respectively, which are higher than those obtained using the pure ZnO model. However, in both the Gai(oct) and Gai(tet) models, an increase in effective mass resulted in a decrease in carrier mobility, thereby reducing electrical conductivity. In addition, interestitial Ga atoms within the ZnO crystal reduced transmittance significantly.