  In this article, we introduce the notion of Lie triple centralizer as
follows. Let $\mathcal{A}$ be an algebra, and $\phi:\mathcal{A}\to\mathcal{A}$
be a linear mapping. we say $\phi$ is a Lie triple centralizer whenever
$\phi([[a,b],c])=[[\phi(a),b],c]$ for all $a,b,c\in\mathcal{A}$. Then we
characterize the general form of Lie triple centralizers on generalized matrix
algebra $\mathcal{U}$ and under some mild conditions on $\mathcal{U}$, we
present the necessary and sufficient conditions for Lie triple centralizers to
be proper. As an application of our results, we characterize generalized Lie
triple derivations on generalized matrix algebras.
