  We consider the lightest Higgs boson in naturally R-parity conserving
supersymmetric left-right models. We obtain an upper bound on the tree level
mass of this lightest Higgs boson. This upper bound depends on the $SU(2)_L$
and $SU(2)_R$ gauge couplings, and the vacuum expectation values of bidoublet
Higgs fields, which are needed to break $SU(2)_L\times U(1)_Y$. The upper bound
does not depend on either the $SU(2)_R$ breaking scale or the supersymmetry
breaking scale. We evaluate the bound numerically by assuming that the theory
remains perturbative upto some scale $\Lambda$. We find that the bound can be
considerably larger than in MSSM. The dominant radiative corrections to the
upper bound due to top-stop and bottom-sbottom systems are of the same form as
in the minimal supersymmetric standard model.
