  The existence of the neutrino mass and flavor mixing have been experimentally
verified. These phenomena strongly motivate to extend the Standard Model (SM).
Amongst many possibilities, a simple and interesting extension of the SM can be
investigated using a general U$(1)_X$ extension of the SM gauge group.
Demanding the cancellation of the gauge and mixed gauge gravity anomalies,
three right handed neutrinos are introduced in this model where the U$(1)_X$
charge assignment becomes a linear combination of U$(1)_{\rm{B-L}}$ and
U$(1)_Y$ hyper-charges. After the U$(1)_X$ breaking, an additional neutral
gauge boson, $Z^\prime$ is evolved and the neutrino mass is generated by the
seesaw mechanism. In such a model we investigate the properties of a Dark
Matter (DM) candidate which is a massive weakly interacting particle and Dirac
type in nature. The stability of the DM is protected by its U$(1)_X$ charge.
Using the current bounds on the search results of $Z^\prime$ at the Large
Hadron Collider (LHC) and the dark matter relic abundance we find a
phenomenologically viable parameter space of our scenario.
