  We discuss gauge mediated supersymmetry breaking models which explain the
observed muon anomalous magnetic moment and the Higgs boson mass
simultaneously. The successful explanation requires the messenger sector which
violates the relation motivated by the grand unification theory (GUT). The
naive violation of the GUT relation, however, ends up with the CP problem. We
propose a model in which the phases of the gaugino masses are aligned despite
the violation of the GUT relation. We also consider a model which generates the
$\mu$-term and the additional Higgs soft masses squared without causing CP
violation. As a result, we find a successful model which explains the muon
anomalous magnetic moment and the Higgs boson mass. The model is also free from
the CP, flavor-changing neutral current and the lepton flavor violation
problems caused by the subdominant gravity mediation effects.
