In this paper, we establish two gap theorems for ends of smooth metric measure space
(
M
n
,
g
,
e
−
f
d
v
)
(M^n, g,e^{-f}dv)
with the Bakry-Émery Ricci tensor
Ric
f
≥
−
(
n
−
1
)
\operatorname {Ric}_{f}\!\ge -(n-1)
in a geodesic ball
B
o
(
R
)
B_{o}(R)
with radius
R
R
and center
o
∈
M
n
o\in M^n
. When
Ric
f
≥
0
\operatorname {Ric}_{f}\ge 0
and
f
f
has some degeneration outside
B
o
(
R
)
B_{o}(R)
, we show that there exists an
ϵ
=
ϵ
(
n
,
sup
B
o
(
1
)
|
f
|
)
\epsilon =\epsilon (n,\sup _{B_{o}(1)}|f|)
such that such a space has at most two ends if
R
≤
ϵ
R\le \epsilon
. When
Ric
f
≥
1
2
\operatorname {Ric}_{f}\ge \frac 12
and
f
(
x
)
≤
1
4
d
2
(
x
,
B
o
(
R
)
)
+
c
f(x)\le \frac 14d^2(x,B_{o}(R))+c
for some constant
c
>
0
c>0
outside
B
o
(
R
)
B_{o}(R)
, we can also get the same gap conclusion.