  We consider an $SU(3)_c \otimes SU(2)_L \otimes SU(2)_R \otimes U(1)_{B-L}$
left-right symmetric model with three Higgs scalars including an $SU(2)_L$
doublet, an $SU(2)_R$ doublet and an $SU(2)_L \otimes SU(2)_R$ bidoublet. In
addition to usual SU(2)-doublet fermions, our model contains SU(2)-triplet
fermions with Majorana masses. The neutral components of the left-handed
triplets can contribute a canonical seesaw while the neutral components of the
right-handed triplets associated with the right-handed neutrinos can contribute
a double/inverse-type seesaw. Our model can be embedded into an SO(10) grand
unification theory where the triplets belong to the $45=(1,3,1,0) \oplus
(1,1,3,0)\oplus ...$ representations.
