  We consider an extended model of DBI massive gravity by generalizing the
fiducial metric to be an induced metric on the brane corresponding to a domain
wall moving in five-dimensional Schwarzschild-Anti-de Sitter spacetime. The
model admits all solutions of FLRW metric including flat, closed and open
geometries while the original one does not. The background solutions can be
divided into two branches namely self-accelerating branch and normal branch.
For the self-accelerating branch, the graviton mass plays the role of
cosmological constant to drive the late-time acceleration of the universe. It
is found that the number degrees of freedom of gravitational sector is not
correct similar to the original DBI massive gravity. There are only two
propagating degrees of freedom from tensor modes. For normal branch, we
restrict our attention to a particular class of the solutions which provides an
accelerated expansion of the universe. It is found that the number of degrees
of freedom in the model is correct. However, at least one of them is ghost
degree of freedom which always present at small scale implying that the theory
is not stable.
