In this paper, the containment control problem of the second-order multi-agent systems (MASs) with general noise over directed topology is investigated. General noise, which may be the mixture of colored and white noise, is introduced to model the perturbation of MASs. Since constructing an anti-perturbed distributed controller for concerned MASs is difficult, we attend to use the perturbation tolerant character of the convex hull spanned by multiple leaders in the containment control problems of MASs. To this end, the hierarchical topology structure of MASs is used, which can largely reduce the communication loads and computational complexity. It is shown that the MASs are noise-to-state stable and the state of the MASs has an asymptotic gain in the mean square based on random differential equations (RDEs) theorem framework. Moreover, the relative hierarchical topology reconfiguration algorithm is given based on which the system can withstand stronger noise and all followers gradually converge to the convex hull formed by the leaders of the respective level. Finally, the numerical simulation is carried out to substantiate the feasibility of the proposed control theory.