Summary: ``In this paper, we focus on high-order approximate solutions of $(N+1)$-level systems with near-resonance control over a long period of time. A high-order renormalization group (RG) method with rigorous proof is developed to deal with such open quantum systems. By constructing high-order RG equations, we obtained the high-order long-time RG approximate solutions of $(N+1)$-level systems in several kinds of near-resonance cases. The numerical simulation results show that our high-order RG method has the same accuracy as the fourth-order Runge-Kutta method in $O(1)$ time scale but more reliable in $O(\frac1\varepsilon)$ time scale.''