  Many inflation theories predict that the primordial power spectrum is scale
invariant. The amplitude of the power spectrum can be constrained by different
observations such as the cosmic microwave background (CMB), Lyman-$\alpha$,
large-scale structures and primordial black holes (PBHs). Although the
constraints from the CMB are robust, the corresponding scales are very large
($10^{-4}<k<1 \mathrm{Mpc^{-1}}$). For small scales ($k > 1
\mathrm{Mpc^{-1}}$), the research on the PBHs provides much weaker limits.
Recently, ultracompact dark matter minihalos (UCMHs) was proposed and it was
found that they could be used to constraint the small-scale primordial power
spectrum. The limits obtained by the research on the UCMHs are much better than
that of PBHs. Most of previous works focus on the dark matter annihilation
within the UCMHs, but if the dark matter particles do not annihilate the decay
is another important issue. In previous work~\cite{EPL}, we investigated the
gamma-ray flux from the UCMHs due to the dark matter decay. In addition to
these flux, the neutrinos are usually produced going with the gamma-ray photons
especially for the lepton channels. In this work, we studied the neutrino flux
from the UCMHs due to the dark matter decay. Finally, we got the constraints on
the amplitude of primordial power spectrum of small scales.
