This paper presents a hybrid algorithm for the petascale global simulation of atmospheric dynamics on Tianhe-2, the world's current top-ranked supercomputer developed by China's National University of Defense Technology (NUDT). Tianhe-2 is equipped with both Intel Xeon CPUs and Intel Xeon Phi accelerators. A key idea of the hybrid algorithm is to enable flexible domain partition between an arbitrary number of processors and accelerators, so as to achieve a balanced and efficient utilization of the entire system. We also present an asynchronous and concurrent data transfer scheme to reduce the communication overhead between CPU and accelerators. The acceleration of our global atmospheric model is conducted to improve the use of the Intel MIC architecture. For the single-node test on Tianhe-2 against two Intel Ivy Bridge CPUs (24 cores), we can achieve 2.07×, 3.18×, and 4.35× speedups when using one, two, and three Intel Xeon Phi accelerators respectively. The average performance gain from SIMD vectorization on the Intel Xeon Phi processors is around 5× (out of the 8× theoretical case). Based on successful computation-communication overlapping, large-scale tests indicate that a nearly ideal weak-scaling efficiency of 93.5% is obtained when we gradually increase the number of nodes from 6 to 8,664 (nearly 1.7 million cores). In the strong-scaling test, the parallel efficiency is about 77% when the number of nodes increases from 1,536 to 8,664 for a fixed 65,664 × 5,664 × 6 mesh with 77.6 billion unknowns.