  If we assume that we live in the center of a spherical inhomogeneous
universe, we can explain the apparent accelerating expansion of the universe
without introducing the unknown dark energy or modifying gravitational theory.
Direct measurement of the cosmic acceleration can be a powerful tool in
distinguishing $\Lambda$CDM and the inhomogeneous models. If $\Lambda$CDM is
the correct model, we have shown that DECIGO/BBO has sufficient ability to
detect the positive redshift drift of the source by observing gravitational
waves from neutron star binaries for 5-10 years. This enables us to rule out
any Lema\^itre-Tolman-Bondi (LTB) void model with monotonically increasing
density profile. Furthermore, by detecting the positive redshift drift at
$z\sim 0$, we can even rule out generic LTB models unless we allow
unrealistically steep density gradient at $z\sim 0$. We also show that the
measurement accuracy is slightly improved when we consider the joint search of
DECIGO/BBO and the third generation Einstein Telescope. This test can be
performed with GW observations alone without any reference to electromagnetic
observations.
