  We propose two Type-II seesaw scenarios for the neutrino mass matrix in the
left-right symmetric model, in which the Higgs triplet Yukawa coupling matrix
takes the appealing Friedberg-Lee texture. We show that the nearly
tri-bimaximal neutrino mixing pattern, which is especially favored by current
neutrino oscillation data, can be obtained from both scenarios. We also show
that the cosmological baryon number asymmetry can naturally be interpreted in
these two scenarios via the flavor-independent leptogenesis mechanism.
