The combination of three-dimensional integrated circuits (3D ICs) and Networks-on-Chip (NoCs) offers considerable performance improvements to Chip MultiProcessors (CMPs). Since on-chip communication is critical to the performance of the NoC-based systems, designing efficient routing methods is highly desirable. This paper presents a new adaptive and deadlock-free routing method addressing the 3D mesh-based NoCs. From a turn model?s point of view, the proposed technique strives to maximize the degree of adaptiveness by minimizing the number of prohibited turns. Uneven degree of adaptiveness degrades the performance of the network to a high extent. As a result, the proposed method exploits distinct sets of rules for different planes so that a balanced traffic distribution can be achieved and the hotspots are less likely to be created. Based on the simulation results, the proposed routing method turns out to be a valuable asset for the traffic distribution across the network.