We use the Higgs coupling and the muon anomalous magnetic moment measurements to constrain the parameter space of the natural supersymmetry in the generalized minimal supergravity (GmSUGRA) model. We scan the parameter space of the GmSUGRA model with small electroweak fine-tuning measure (). The parameter space after applying various sparticle mass bounds; Higgs mass bounds; B-physics bounds; the muon magnetic moment constraint; and the Higgs coupling constraint from measurements at HL-LHC, ILC, and CEPC is shown in the planes of various interesting model parameters and sparticle masses. Our study indicates that the Higgs coupling and muon anomalous magnetic moment measurements can constrain the parameter space effectively. It is shown that , consistent with all constraints, and having supersymmetric contributions to the muon anomalous magnetic moment within can be achieved. The precision of and measurements at CEPC can bound to be above 1.2 TeV and 1.1 TeV respectively. The combination of the Higgs coupling measurement and muon anomalous magnetic moment measurement constrain the e˜R mass to be in the range from 0.6 TeV to 2 TeV. The range of both e˜L and ν˜e masses is 0.4 TeV–1.2 TeV. In all cases, the χ˜10 mass needs to be small (mostly ). The comparison of bounds in the plane shows that the Higgs coupling measurement is complementary to the direct collider searches for heavy Higgs when constraining the natural SUSY. A few mass spectra in the typical region of parameter space after applying all constraints are shown as well.