  Within the framework of the Aubry-Andre model, one kind of self-dual
quasiperiodic lattice, it is known that a sharp transition occurs from
\emph{all} eigenstates being extended to \emph{all} being localized. The common
perception for this type of quasiperiodic lattice is that the self-duality
excludes the appearance of the mobility edge separating localized from extended
states. In this work, we propose a multi-chromatic quasiperiodic lattice model
retaining the self-duality identical to the Aubry-Andre model, and demonstrate
numerically the occurrence of the localization-delocalization transition with
definite mobility edges. This contrasts with the Aubry-Andre model. As a
result, the diffusion of wave packet exhibits a transition from ballistic to
diffusive motion, and back to ballistic motion. We point out that experimental
realizations of the predicted transition can be accessed with light waves in
photonic lattices and matter waves in optical lattices.
