Spectral response of Schottky photodiodes consisting of a MgxZn1-xO (x <= 0.43) thin film and a transparent conducting polymer, poly(3,4-ethylenedioxythiophene) poly(styrenesulfonate), was characterized under a zero-bias condition at room temperature. The cut-off wavelength in each photodiode was systematically tuned by Mg content (x), while its high quantum efficiency was kept near unity. The steepness in the photo-response around the cut-off wavelength was maintained for higher x samples, implying a small alloy broadening effect in this system.