  We theoretically predict a giant quantized Goos-H\"{a}nchen (GH) effect on
the surface of graphene in quantum Hall regime. The giant quantized GH effect
manifests itself as an angular shift whose quantized step reaches the order of
mrad for light beams impinging on a graphene-on-substrate system. The quantized
GH effect can be attributed to quantized Hall conductivity, which corresponds
to the discrete Landau levels in quantum Hall regime. We find that the
quantized step can be greatly enhanced for incident angles near the Brewster
angle. Moreover, the Brewster angle is sensitive to the Hall conductivity, and
therefore the quantized GH effect can be modulated by the Fermi energy and the
external magnetic field. The giant quantized GH effect offers a convenient way
to determine the quantized Hall conductivity and the discrete Landau levels by
a direct optical measurement.
