  In this paper, we apply the statefinder diagnostic to the cosmology with the
Abnormally Weighting Energy hypothesis (AWE cosmology), in which dark energy in
the observational (ordinary matter) frame results from the violation of weak
equivalence principle (WEP) by pressureless matter. It is found that there
exist closed loops in the statefinder plane, which is an interesting
characteristic of the evolution trajectories of statefinder parameters and can
be used to distinguish AWE cosmology from the other cosmological models.
