It is very important to develop high performance computing algorithm and software adapting China heterogeneous supercomputer. This has also great significance in minimizing the gap between China's HPC hardware and HPC software. Firstly, the article briefly introduces current trend and challenges of high-performance computing application software and analyzes computing algorithm characteristics of various typical high performance computing applications including N-body simulation in computing cosmology, earth system model, computational material phase field dynamics, molecular dynamics, quantum chemistry, and lattice QCD. Secondly, solution to use domestic heterogeneous computing system has been discussed and typical application algorithms, common questions of software including core algorithm, development of algorithm, strategies of optimizing codes have been summarized as well. Finally, a summary of high-performance computing algorithms and software for heterogeneous computing is given.