  In the present work, we study the possible production of the light neutral
gauge boson (Z$^{\prime}$) candidates, which originated from a simplified-model
scenario based on the Mono-Z$^{\prime}$ model, in association with dark matter.
This study has been performed by studying events with dimuon plus missing
transverse energy produced in the simulated electron-positron collisions at the
foreseen International Linear Collider (ILC), operating at 500 GeV center of
mass energy and integrated luminosity of 1000 fb$^{-1}$. In case no new physics
has been discovered, we set upper limits at 95\% confidence level on the masses
of various particles in the model as, spin-1 (Z$^{\prime}$), as well as the
fermionic dark matter.
