  We study natural supersymmetry in the Generalized Minimal Supergravity
(GmSUGRA). For the parameter space with low energy electroweak fine-tuning
measures less than 50, we are left with only the $Z$-pole, Higgs-pole and
Higgsino LSP scenarios for dark matter (DM). We perform the focused scans for
such parameter space and find that it satisfies various phenomenological
constraints and is compatible with the current direct detection bound on
neutralino DM reported by the LUX experiment. Such parameter space also has
solutions with correct DM relic density besides the solutions with DM relic
density smaller or larger than 5$\sigma$ WMAP9 bounds. We present five
benchmark points as examples. In these benchmark points, gluino and the first
two generations of squarks are heavier than 2 TeV, stop $\tilde t_{1,2}$ are in
the mass range $[1,2]$ TeV, while sleptons are lighter than 1 TeV. Some part of
the parameter space can explain the muon anomalous magnetic moment within
3$\sigma$ as well. We also perform the collider study of such solutions by
implementing and comparing with relevant studies done by the ATLAS and CMS
Collaborations. We find that the points with Higgsino dominant
$\tilde{\chi}_2^0/\tilde{\chi_1}^\pm$ mass up to $300$ GeV are excluded in
$Z$-pole scenario while for Higgs-pole scenario, the points with
$\tilde{\chi}_2^0$ mass up to $460$ GeV are excluded. We also notice that the
Higgsino LSP points in our present scans are beyond the reach of present LHC
searches. Next, we show that for both the $Z$-pole and Higgs-pole scenarios,
the points with electroweak fine-tuning measure around 20 do still survive.
