  We explored the sparticle mass spectrum in light of the muon g-2 anomaly and
the little hierarchy problem in a class of gauge mediated supersymmetry
breaking model. Here the messenger fields transform in the adjoint
representation of the Standard Model gauge symmetry. To avoid unacceptably
light right-handed slepton masses the standard model is supplemented by
additional U(1)_B-L gauge symmetry. Considering a non-zero U(1)_B-L D-term
leads to an additional contribution to the soft supersymmetry breaking mass
terms which makes the right-handed slepton masses compatible with the current
experimental bounds. We show that in the framework of Lambda_{3}<0 and mu < 0,
the muon g-2 anomaly and the observed 125 GeV Higgs boson mass a can be
simultaneously accommodated. The slepton masses in this case are predicted to
lie in the few hundred GeV range, which can be tested at LHC. Despite the heavy
colored spectrum the the little hierarchy problem in this model can be
ameliorated and electroweak fine tuning parameter can be as low as 10 or so.
