Let
(
X
,
ω
)
(X,\omega )
be a compact Kähler manifold of complex dimension
n
n
and
(
L
,
h
)
(L,h)
be a holomorphic line bundle over
X
X
. The line bundle mean curvature flow was introduced by Jacob-Yau in order to find deformed Hermitian-Yang-Mills metrics on
L
L
. In this paper, we consider the stability of the line bundle mean curvature flow. Suppose there exists a deformed Hermitian Yang-Mills metric
h
^
\hat h
on
L
L
. We prove that the line bundle mean curvature flow converges to
h
^
\hat h
exponentially in
C
∞
C^\infty
sense as long as the initial metric is close to
h
^
\hat h
in
C
2
C^2
-norm.