The wavefront quality of white-light supercontinuum is crucial for applications like waveform synthesis or imaging. It has been here generated by 1030 nm centered sub-picosecond pulses in YAG and characterized with a Shack-Hartmann wavefront sensor across different parts of the spectrum. It shows a good wavefront quality of λ/11 and little dependence on the wavelength of the supercontinuum. The wavefront deformations are transferred from the driver laser wavefront to the supercontinuum independently of the wavelength.