We study the muon anomalous magnetic moment (muon g-2) and the Higgs boson
mass in a simple extension of the minimal supersymmetric (SUSY) Standard Model
with extra vector-like matters, in the frameworks of gauge mediated SUSY
breaking (GMSB) models and gravity mediation (mSUGRA) models. It is shown that
the deviation of the muon g-2 and a relatively heavy Higgs boson can be
simultaneously explained in large tan-beta region. (i) In GMSB models, the
Higgs mass can be more than 135 GeV (130 GeV) in the region where muon g-2 is
consistent with the experimental value at the 2 sigma (1 sigma) level, while
maintaining the perturbative coupling unification. (ii) In the case of mSUGRA
models with universal soft masses, the Higgs mass can be as large as about 130
GeV when muon g-2 is consistent with the experimental value at the 2 sigma
level. In both cases, the Higgs mass can be above 140 GeV if the g-2 constraint
is not imposed.Comment: 26 pages; 7 figures; corrected typos; minor change