  We identify a parameter region where the mass of the lightest CP-even Higgs
boson resides in $124.4-126.8$ GeV, and at the same time the degree of tuning a
Higgsino-mass parameter (so-called $\mu$-parameter) is relaxed above 10% in the
minimal supersymmetric standard model (MSSM) with soft supersymmetry breaking
terms, by solving the full set of one-loop renormalization group equations
numerically. It is found that certain nonuniversal values of gaugino-mass
parameters at the so-called grand unification theory (GUT) scale $\sim 10^{16}$
GeV are important ingredients for the MSSM to predict, without a severe
fine-tuning, the Higgs boson mass $\sim 125$ GeV indicated by recent
observations at the Large Hadron Collider. We also show a typical superparticle
spectrum in this parameter region.
