In this paper, we study complete self-shrinkers in Euclidean space and prove that an
n
n
-dimensional complete self-shrinker with polynomial volume growth in Euclidean space
R
n
+
1
\mathbb {R}^{n+1}
is isometric to either
R
n
\mathbb {R}^{n}
,
S
n
(
n
)
S^{n}(\sqrt {n})
, or
R
n
−
m
×
S
m
(
m
)
\mathbb {R}^{n-m}\times S^m (\sqrt {m})
,
1
≤
m
≤
n
−
1
1\leq m\leq n-1
, if the squared norm
S
S
of the second fundamental form is constant and satisfies
S
>
10
7
S>\frac {10}{7}
.