  We theoretically investigate light propagation and Anderson localization in
one-dimensional disordered superlattices composed of dielectric stacks with
graphene sheets in between. Disorder is introduced either on graphene material
parameters ({\it e.g.} Fermi energy) or on the widths of the dielectric stacks.
We derive an analytic expression for the localization length $\xi$, and compare
it to numerical simulations using transfer matrix technique; a very good
agreement is found. We demonstrate that the presence of graphene may strongly
attenuate the anomalously delocalised Breswter modes, and is at the origin of a
periodic dependence of $\xi$ on frequency, in contrast to the usual asymptotic
decay, $\xi \propto \omega^{-2}$. By unveiling the effects of graphene on
Anderson localization of light, we pave the way for new applications of
graphene-based, disordered photonic devices in the THz spectral range.
