3D Network-on-Chips (NoCs) is an efficient solution to multi-core communications. The routing algorithm has become a critical challenge for higher performance of NoCs. Performance of traditional methods based on the turn models degrades when the network gets saturated. To improve network stability after saturation, in this paper, a novel deadlock-free Path-Diversity-Aware Hybrid Planar Adaptive Routing (PDA-HyPAR) algorithm without using virtual channels is proposed. In this method, different routing rules are exploited in different XY-planes. And planar adaptive routing strategy is proposed to balance the network loads. We analyze the path-diversity theoretically and the experimental results show that the PDA-HyPAR is effective even if network load becomes heavy.