  The small-scale crisis is one of the most outstanding puzzles in modern
cosmology and astrophysics. It may imply a suppression of matter perturbation
at small scale. In this work, by taking into account of the gravitational
effects from the non-equilibrium production of DM, we propose a new mechanism,
which can realize such desired suppression and alleviate the crisis within the
framework of cold dark matter (DM) and simple inflation. Moreover, in this new
mechanism, we establish a novel relation between the particle mass of DM,
$m_\chi$, and the critical scale of suppression, $k_\star^{-1}$. As
$k_\star^{-1}$ will be further constrained in future astrophysical
observations, $m_\chi$ can be constrained accordingly with this relation. It
thus provides a new method in complementary to other existing strategies of
determining $m_\chi$. Furthermore, to illustrate our theoretical prediction, we
consider a suppression at $k_\star^{-1}=1~\text{kpc}$ that can partially
alleviate the small-scale crisis, and obtain $m_\chi=2.2~\text{MeV}$ for
realizing such suppression. Then we plot the power spectrum of linear matter
perturbation for this case, and illustrate a salient feature of the suppression
that can serves a smoking-gun signature of this new mechanism in future
observations.
