The Standard Model Higgs boson with the nonminimal coupling to the gravitational curvature can drive cosmological inflation. We study this type of inflationary scenario in the context of supergravity. We first point out that it is naturally implemented in the minimal supersymmetric SU(5) model, and hence virtually in any GUT models. Next we propose another scenario based on the Minimal Supersymmetric Standard Model supplemented by the right-handed neutrinos. These models can be tested by new observational data from the Planck satellite experiments within a few years.