  In the framework of an nonuniversal $U(1)'$ extension of the standard model,
we propose an scalar candidate for cold dark matter which exhibits interactions
with ordinary matter through Higgs and gauge bosons. Using limits from low
energy observables, we find constraints on the new physics parameters of the
model associated to the extra abelian symmetry, in particular, the mass of the
additional neutral gauge boson $Z'$ and the new gauge coupling constant. We
found that for the lower experimental limit $M_{Z'}=3$ TeV constrained by
direct research at LHC, the ratio between the $U(1)'$ and $SU(2)_L$ gauge
coupling constants is around $0.4$. Taking into account this limit and the
observable relic density of the Universe, we search for new constraints on the
mass of the dark matter particle of the model. We found that for a higgsphobic
model, the mass of the scalar dark matter must be $M_{\sigma}=70$ GeV. We also
found different kinematical threshold and resonances that enhance the
dispersion of dark matter into ordinary matter for different regions of the
space of parameters of the model, obtaining masses as low as $1.3$ GeV and as
large as $125$ GeV with not allowed intermediate regions due to resonances.
