Summary: Let \(p:X\to B\) be a locally trivial principal \(G\)-bundle and \(\widetilde{p}:\widetilde{X}\to B\) be a locally trivial principal \(\widetilde{G}\)-bundle. In this paper, by using the structure of principal bundles according to transition functions, we show that \(\widetilde{G}\) is a covering group of \(G\) if and only if \(\widetilde{X}\) is a covering space of \(X\). Then we conclude that a topological space \(X\) with non-simply connected universal covering space has no connected locally trivial principal \(\pi(X,x_0)\)-bundle, for every \(x_0\in X\).