  A simple model for the explanation of the muon anomalous magnetic moment was
proposed by the present authors within the context of the minimal
supersymmetric standard model [1607.05705, 1608.06618]: "Higgs-anomaly
mediation". In the setup, squarks, sleptons, and gauginos are massless at
tree-level, but the Higgs doublets get large negative soft supersymmetry (SUSY)
breaking masses squared $m_{H_u}^2 \simeq m_{H_d}^2 < 0$ at a certain energy
scale, $M_{\rm inp}$. The sfermion masses are radiatively generated by anomaly
mediation and Higgs-loop effects, and gaugino masses are solely determined by
anomaly mediation. Consequently, the smuons and bino are light enough to
explain the muon $g-2$ anomaly while the third generation sfermions are heavy
enough to explain the observed Higgs boson mass. The scenario avoids the SUSY
flavor problem as well as various cosmological problems, and is consistent with
the radiative electroweak symmetry breaking. In this paper, we show that,
although the muon $g-2$ explanation in originally proposed Higgs-anomaly
mediation with $M_{\rm inp}\sim 10^{16}\,$GeV is slightly disfavored by the
latest LHC data, the muon $g-2$ can still be explained at $1\sigma$ level when
Higgs mediation becomes important at the intermediate scale, $M_{\rm inp} \sim
10^{12}\,$GeV. The scenario predicts light SUSY particles that can be fully
covered by the LHC and future collider experiments. We also provide a simple
realization of $m_{H_u}^2 \simeq m_{H_d}^2 < 0$ at the intermediate scale.
