  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. The model
has three right-handed neutrinos with identical $B-L$ charges, and can
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. We obtain the mass spectra of all sectors and for the scalar one we
also give the flat directions allowed by the model.
