  We study the cosmological perturbations of the new bi-metric gravity proposed
by Hassan and Rosen \cite{hasan} as a representation of massive gravity. The
mass term in the model, in addition of ensuring ghost freedom for both metrics,
causes the two scale factors to mix at the cosmological level and this affects
the cosmological perturbation of the model. We find two combinations
corresponding to the entropy and adiabatic perturbations of the theory. In this
sense we show that the adiabatic perturbations could be a source for the
entropy perturbations. So in addition to the adiabatic perturbations, entropy
perturbations can also be present in this theory. We also show that the
adiabatic perturbations are not constant at the super horizon scales, implying
that the theory could not be used to describe the inflationary epoch, even if
it can impose some corrections to the standard inflationary scenarios.
