  Recently the ATLAS and CMS collaborations presented preliminary results of
Standard Model Higgs searches and reported excesses of events for a Higgs boson
at 124-126 GeV. Such a Higgs mass can be naturally realized, simultaneously
explaining the muon g-2 anomaly, in gauge-mediated SUSY breaking models with
extra vector-like matters. Upper bounds are obtained on the gluino mass,
m_{\tilde g}\lesssim 1.2 (1.8) TeV, and on the extra vector-like quark mass,
M_{Q'} \lesssim 1.0 (1.8) GeV, in the parameter region where the Higgs boson
mass is 124-126 GeV and the muon g-2 is consistent with the experimental value
at the 1 sigma (2 sigma) level. The LHC prospects are explored in the parameter
region. It is found that some of the regions are already excluded by the LHC,
and most of the parameter space is expected to be covered at \sqrt{s} = 14 TeV.
A study on the extra vector-like quarks, especially current bounds on their
masses and prospects for future searches, is also included.
