In this paper, we study complete self-shrinkers in Euclidean space and prove that an
n
n
-dimensional complete self-shrinker 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
S
k
(
k
)
×
R
n
−
k
S^k (\sqrt {k})\times \mathbb {R}^{n-k}
,
1
≤
k
≤
n
−
1
1\leq k\leq n-1
, if the squared norm
S
S
of the second fundamental form,
f
3
f_3
are constant and
S
S
satisfies
S
>
1.83379
S>1.83379
. We should remark that the condition of polynomial volume growth is not assumed.