  We derive the partition function of N=4 supersymmetric Yang-Mills theory on
orbifold-$T^4/{\bf Z}_2$. In classical geometry, K3 surface is constructed from
the orbifold-$T^4/{\bf Z}_2$. Along the same way as the orbifold construction,
we construct the partition function of K3 surface from orbifold-$T^4/{\bf
Z}_2$. The partition function is given by the product of the contribution of
the untwisted sector of $T^4/{\bf Z}_2$, and that of the twisted sector of
$T^4/{\bf Z}_2$ i.e., ${\cal O}(-2)$ curve blow-up formula.
