Second-harmonic generation has been studied for fundamental wavelengths from 720 to 1100 nm on high-quality ZnO thin films deposited on sapphire substrates by laser molecular beam epitaxy. The second-order nonlinear susceptibility components increase dramatically as the second-harmonic frequency approaches the ZnO bandgap. The increase is most likely due to a resonance of the second-harmonic frequency with the critical point transition associated with the direct bandgap transition. Large second-order nonlinear susceptibility components were determined to have a nonresonant background value of -83.7 pm V for d, 14.7 pm V for d and 15.2 pm V for d for a fundamental wavelength of 1064 nm. The value of d for the film was as high as 14 times that of bulk material in the nonresonant region. The difference in values between the second nonlinear coefficients of the bulk and the film may originate from the microcrystallite structure.