  Gluino-SUGRA ($\tilde{g}$SUGRA), which is an economical extension of the
predictive mSUGRA, adopts much heavier gluino mass parameter than other
gauginos mass parameters and universal scalar mass parameter at the unification
scale. It can elegantly reconcile the experimental results on the Higgs boson
mass, the muon $g-2$, the null results in search for supersymmetry at the LHC
and the results from B-physics. In this work, we propose several new ways to
generate large gaugino hierarchy (i.e. $M_3\gg M_1,M_2$) for $\tilde{g}$SUGRA
model building and then discuss in detail the implications of the new muon
$g-2$ results with the updated LHC constraints on such $\tilde{g}$SUGRA
scenarios. We obtain the following observations: (i) For the most interesting
$M_1=M_2$ case at the GUT scale with a viable bino-like dark matter, the
$\tilde{g}$SUGRA can explain the muon $g-2$ anomaly at $1\sigma$ level and be
consistent with the updated LHC constraints for $6\leq M_3/M_1 \leq 9$ at the
GUT scale; (ii) For $M_1:M_2=5:1$ at the GUT scale with wino-like dark matter,
the $\tilde{g}$SUGRA model can explain the muon $g-2$ anomaly at $2\sigma$
level and be consistent with the updated LHC constraints for $3\leq M_3/M_1
\leq 3.2$ at the GUT scale; (iii) For $M_1:M_2=3:2$ at the GUT scale with mixed
bino-wino dark matter, the $\tilde{g}$SUGRA model can explain the muon $g-2$
anomaly at $1\sigma$ level and be consistent with the updated LHC constraints
for $6.9\leq M_3/M_1 \leq 7.5$ at the GUT scale. Although the choice of heavy
gluino will always increase the FT involved, some of the $1\sigma/2\sigma$
survived points of $\Delta a_\mu^{combine}$ can still allow low EWFT of order
several hundreds and be fairly natural. Constraints from (dimension-five
operator induced) proton decay are also discussed.
