Ga doped ZnO thin films are prepared on glass substrates by RF magnetron co-sputtering method in which Ga dopant concentrations are varied systematically. Resulting GaZnO films show the optical band gap widening behavior and a sharp rise of the band gap at ~3% doping level, which is attributed to Burstein-Moss effect. The electrical properties are best improved near the ~3% doping concentration at which carrier mobility displays a maximum value.