  In this work, we implement a complex scalar Dark Matter (DM) candidate in a
$U(1)_{B-L}$ gauge extension of the Standard Model. The model contains three
right handed neutrinos with different quantum numbers and a rich scalar sector,
with extra doublets and singlets. In principle, these extra scalars can have
VEVs ($V_{\Phi}$ and $V_{\phi}$ for the extra doublets and singlets,
respectively) belonging to different energy scales. In the context of
$\zeta\equiv\frac{V_{\Phi}}{V_{\phi}}\ll1$, which allows to obtain naturally
light active neutrino masses and mixing compatible with neutrino experiments,
the DM candidate arises by imposing a $Z_{2}$ symmetry on a given complex
singlet, $\phi_{2}$, in order to make it stable. After doing a study of the
scalar potential and the gauge sector, we obtain all the DM dominant processes
concerning the relic abundance and direct detection. Then, for a representative
set of parameters, we found that a complex DM with mass around $200$ GeV, for
example, is compatible with the current experimental constraints without
resorting to resonances. However, additional compatible solutions with heavier
masses can be found in vicinities of resonances. Finally, we address the issue
of having a light CP-odd scalar in the model showing that it is safe concerning
the Higgs and the $Z_{\mu}$ boson invisible decay widths, and also the energy
loss in stars astrophysical constraints.
