Let
G
G
be a connected, simple algebraic group over an algebraically closed field. There is a partition of the wonderful compactification
G
¯
\bar {G}
of
G
G
into finite many
G
G
-stable pieces, which was introduced by Lusztig. In this paper, we will investigate the closure of any
G
G
-stable piece in
G
¯
\bar {G}
. We will show that the closure is a disjoint union of some
G
G
-stable pieces, which was first conjectured by Lusztig. We will also prove the existence of cellular decomposition if the closure contains finitely many
G
G
-orbits.