In this note we present a short proof of the following result by Zhou, Liu and Xu. Let G be a graph of order n, and let a and b be two integers with 1 $leq$ a < b and b $geq$ 3, and let g and f be two integer-valued functions defined on V(G) such that a $leq$ g(x) < f(x) $leq$ b for each $x;{in};V(G)$ and f(V(G)) - V(G) even. If $n;{geq};frac{(a+b-1)^2+1}{a}$ and $delta(G);{geq};frac{(b-1)n}{a+b-1}$,then G has a connected (g, f)-factor.