  In this paper, we consider the stability of the generalized Lagrangian mean
curvature flow of graph case in the cotangent bundle, which is first defined by
Smoczyk-Tsui-Wang. By new estimates of derivatives along the flow, we weaken
the initial condition and remove the positive curvature condition in
Smoczyk-Tsui-Wang's work. More precisely, we prove that if the graph induced by
a closed $1$-form is a special Lagrangian submanifold in the cotangent bundle
of a Riemannian manifold, then the generalized Lagrangian mean curvature flow
is stable near it.
