ZnO and Co-doped ZnO thin films (3 and 11 at. %) were grown on glass substrates by spin coating method and structurally investigated by X-ray diffraction, X-ray photoelectron spectroscopy and UV-vis absorption spectroscopy. It was established that Co enters into ZnO wurtzite lattice by substitution. The electrical conductivity of undoped and Co-doped ZnO nanocrystalline thin films was measured in the temperature range of 300-425 K. The electrical conduction mechanism of the films is explained on the basis of the multiphonon assisted hopping model with a weak electron phonon coupling. We found that the conductivity first increases with incorporation in ZnO structure of an amount of 3 at. % Co but then it decreases when the amount of Co is increased to 11 at. %. This situation is well explained by the fluctuation in the hopping rate.