  We build a supersymmetric version with $SU(3)_{C}\otimes SU(2)_{L}\otimes
U(1)_{Y^{\prime}}\otimes U(1)_{(B-L)}$ gauge symmetry, where $Y^{\prime}$ is a
new charge and ($B$) and ($L$) are the usual baryonic and leptonic numbers,
respectivelly. The model has three right-handed neutrinos with non identical
$(B-L)$ charges. We will use the superfield formalism in order to build our
lagrangian and it is possible to accommodate all fermion masses at the tree
level. In particular, the type-I seesaw mechanism is implemented for the
generation of the active neutrino masses and also explain the mixing angle at
the fermion sector. There are good candidates to Dark Matter, it can be the
lighest righ-handed neutrinos or lighest right-handed sneutrinos or the lighest
usual scalar field and due a Majorana phase at sneutrinos right-handed masses,
it can induce Leptogenesis in this model.
