In 1970 Lovász gave a necessary and sufficient condition for the existence of a factor F in a graph G such that for each vertex v, g(v) ≤ dF (v) ≤ f (v), where g and f are two integer-valued functions on V (G) with g ≤ f . In this paper, we give a sufficient edge-connectivity condition for the existence of an m-tree-connected factor H in a bipartite graph G with bipartition (X, Y ) such that its complement is m0-tree-connected and for each vertex v, dH. Moreover, we generalize this result to general graphs. As an application, we give sufficient conditions for the existence of tree-connected {g, f }-factors in edge-connected graphs and tough graphs.