The peak fluorescence emission of conventional fluorophores such as organic dyes and inorganic quantum dots is independent of the excitation wavelength. In contrast, the position of the peak fluorescence of graphene oxide (GO) in a polar solvent is heavily dependent on the excitation wavelength. The present work has discovered that the strong excitation wavelength-dependent fluorescence in GO is originated from the "giant red-edge effect", which breaks Kasha's rule. When GO sheets are present in a polar solvent, the solvation dynamics slow down to the same time scale as the fluorescence due to the local environment of the GO sheet. Consequently, the fluorescence peak of GO broadens and red-shifts up to 200 nm with an increase in the excitation wavelength. The giant red-edge effect of GO disappears in a non-polar solvent, leading to a narrow fluorescence peak that is independent of the excitation wavelength. Discovery of the underlying strong excitation wavelength-dependent fluorescence mechanism provides guidelines for the design of graphene oxide-based optical devices.