  Let $G$ be a connected semisimple Lie group with finite centre, and let $M=
\Gamma \backslash G$ be a compact homogeneous manifold. Under a spectral gap
assumption, we show that smooth time-changes of any unipotent flow on $M$ have
polynomial decay of correlations. Our result applies also in the case where $M$
is a finite volume, non-compact quotient under some additional assumptions on
the generator of the time-change. This generalizes a result by Forni and
Ulcigrai (JMD, 2012) for smooth time-changes of horocycle flows on compact
surfaces.
