  In this paper, we introduce the notion of an Okamoto-Painlev\'e pair (S, Y)
which consists of a compact smooth complex surface S and an effective divisor Y
on S satisfying certain conditions. Though spaces of initial values of
Painlev\'e equations introduced by K. Okamoto give examples of Okamoto-Painleve
pairs, we find a new example of Okamoto-Painlev\'e pairs not listed in
\cite{Oka}. We will give the complete classification of Okamoto-Painlev\'e
pairs.
