(Zn,Mg)O (ZMO) thin films doped with Ga $(0~0.03mol\%)$ in the target source were prepared by pulsed laser deposition on c-plane sapphire substrates at $500^{circ}C$, and the effect of Ga contents on the properties of the electrical, optical and crystal properties of the deposited films was investigated. From X-ray diffraction patterns, ZMO film doped with $0.02 mol\%$ Ga showed crystal structure with c-axis preferred orientation, showing only the (0002) and (0004) diffraction peaks. In contrast, ZMO film doped with $Ga=0.03 mol\%$ showed a randomly oriented crystal structure. All the samples were highly transparent, showing the transmittance values of above $85\%$ in the visible region. For all the Ga doped ZMO films, the value of energy band gap was found to be about 3.5 eV, regardless of their Ga contents. From the Hall measurements, the resistivity and the carrier density for the ZMO film doped with $0.01 mol\%$ Ga were about $5 imes10^{-4}Omega-cm$ and $2 imes10^{21}cm^{-3}$, respectively.