  Ho\v{r}ava-Lifshitz gravity is a potentially UV complete theory with
important implications for the very early universe. In particular, in the
presence of spatial curvature it is possible to obtain a non-singular bouncing
cosmology. The bounce is realized as a consequence of higher order spatial
curvature terms in the gravitational action. Here, we extend the study of
linear cosmological perturbations in Ho\v{r}ava-Lifshitz gravity coupled to
matter in the case when spatial curvature is present. As in the case without
spatial curvature, we find that there is no extra dynamical degree of freedom
for scalar metric perturbations. We study the evolution of fluctuations through
the bounce and show that the solutions remain non-singular throughout. If we
start with quantum vacuum fluctuations on sub-Hubble scales in the contracting
phase, and if the contracting phase is dominated by pressure-less matter, then
for $\lambda = 1$ and in the infrared limit the perturbations at late times are
scale invariant. Thus, Ho\v{r}ava-Lifshitz gravity can provide a realization of
the ``matter bounce'' scenario of structure formation.
