High-quality ZnO:Co thin films were synthesized on the sapphire (0001) substrates by pulsed laser deposition. XRD result reveals that the Zn1-xCoxO films are of wurtzite-type crystal structure with x up to x = 0.35. The structural, optical and magnetic properties of ZnO:Co thin films are studied by experiments and theoretical calculations. Electronic structure of ZnO:Co with native defects are studied by the first-principles density functional theory. The experimental data and theoretical data have demonstrated quite good agreement. The optical and magneto-optical properties, namely, on-and off-diagonal conductivity tensor and the transversal Kerr effect (TKE), are calculated for comparison with available experimental data. The origin of observed TKE peaks is discussed..