  We study the spectrum of metric fluctuation in $\kappa$-deformed inflationary
universe. We write the theory of scalar metric fluctuations in the
$\kappa-$deformed Robertson-Walker space, which is represented as a non-local
theory in the conventional Robertson-Walker space. One important consequence of
the deformation is that the mode generation time is naturally determined by the
structure of the $\kappa-$deformation.
  We expand the non-local action in $H^2/\kappa^2$, with $H$ being the Hubble
parameter and $\kappa$ the deformation parameter, and then compute the power
spectra of scalar metric fluctuations both for the cases of exponential and
power law inflations up to the first order in $H^2/\kappa^2$. We show that the
power spectra of the metric fluctuation have non-trivial corrections on the
time dependence and on the momentum dependence compared to the commutative
space results. Especially for the power law inflation case, the power spectrum
for UV modes is weakly blue shifted early in the inflation and its strength
decreases in time. The power spectrum of far-IR modes has cutoff proportional
to $k^3$ which may explain the low CMB quadrupole moment.
