  Numerical calculation of two-loop electroweak corrections to the muon
anomalous magnetic moment ($g$-2) is done based on, on shell renormalization
scheme (OS) and free quark model (FQM). The GRACE-FORM system is used to
generate Feynman diagrams and corresponding amplitudes. Total 1780 two-loop
diagrams and 70 one-loop diagrams composed of counter terms are calculated to
get the renormalized quantity. As for the numerical calculation, we adopt
trapezoidal rule with Double Exponential method (DE). Linear extrapolation
method (LE) is introduced to regularize UV- and IR-divergences and to get
finite values. The reliability of our result is guaranteed by several
conditions. The sum of one and two loop electroweak corrections in this
renormalization scheme becomes $a_\mu^{EW:OS}[1{\rm+}2{\rm -loop}]= 151.2 (\pm
1.0)\times 10^{-11}$, where the error is due to the numerical integration and
the uncertainty of input mass parameters and of the hadronic corrections to
electroweak loops. By taking the hadronic corrections into account, we get
$a_\mu^{EW}[1{\rm+}2 {\rm -loop}]= 152.9 (\pm 1.0)\times 10^{-11}$. It is in
agreement with the previous works given in PDG within errors.
