  We study the cosmological perturbations of the recently proposed extension of
non-linear massive gravity with a scalar field. The added scalar field ensures
a new symmetry on the field space of the theory. The theory has the property of
having a flat dS solution, in contrast to the standard dRGT massive gravity.
The tensor part is the same as that of the standard dRGT and shows
gravitational waves with a time dependent mass which modifies the dispersion
relation. We obtain the curvature perturbation of the model on superhorizon
scales for a specific choice of $\omega=0$ and find that the theory does not
allow a constant curvature perturbation on the superhorizon scales and we have
always a growing mode. The consistency of equations restricts the parameter
space of the theory.
