Zinc oxide (ZnO) bottom-contact thin-film transistors (TFTs) were prepared by the use of injector type atomic layer deposition. Two hybrid gate oxide systems of different polarity polymers with silicon oxide were examined with the aim of improving the properties of the transistors. The mobility and threshold voltage of a ZnO TFT with a poly(4-dimethylsilyl styrene) (Si-PS)/silicon oxide hybrid gate dielectric had values of 0.41 $cm^2/Vs$ and 24.4 V, and for polyimide/silicon oxide these values were 0.41 $cm^2/Vs$ and 24.4 V, respectively. The good hysteresis property was obtained with the dielectric of hydrophobicity. The solid output saturation behavior of ZnO TFTs was demonstrated with a $10^6$ on-off ratio.