  We study bounds on Higgs boson masses from perturbative unitarity in the
Georgi-Machacek model, whose Higgs sector is composed of a scalar isospin
doublet, a real and a complex isospin triplet fields. This model can be
compatible with the electroweak precision data without fine tuning because of
the imposed global SU(2)_R symmetry in the Higgs potential, by which the
electroweak rho parameter is unity at the tree level. All possible two-body
elastic-scattering channels are taken into account to evaluate the S-wave
amplitude matrix, and then the condition of perturbative unitarity is imposed
on the eigenvalues to obtain constraint on the Higgs parameters. Masses of all
scalar bosons turn out to be bounded from above, some of which receive more
strict upper bounds as compared to that in the standard model (712 GeV). In
particular, the upper bound of the lightest scalar boson, whatever it would be,
is about 270 GeV.
