In this paper, we discuss chromatic dispersion properties of transverse Anderson localization optical fiber (TALOF) and their implications on broad band supercontinuum (SC) generation. Our dispersion study reveals a clear correlation between the Anderson localization length and the dispersion properties of highly localized TALOF modes. We demonstrate that the zero dispersion wavelength can be tuned over more than 300 nm within the same fiber by selected excitation of specific modes. We exploit this unique TALOF property, which we validated with rigorous finite-element modeling, to generate multi octave spanning SC ranging from 460–1750 nm, highlighting the great potential of disordered Anderson localization fibers for nonlinear applications.