Abstract: Tianhe supercomputers developed by the National University of Defense Technology won first place in the world's supercomputing TOP500 seven times. To exploit the high efficiency of those systems, the Tianhe team extracted the common key computing methods in large-scale scientific and engineering computing, designed and implemented scalable parallel algorithms for those methods according to the characteristics of the Tianhe supercomputers, and developed the Tianhe parallel algorithm libraries which are an important part of the Tianhe application-support environment. This paper first reviews the development history and system structures of Tianhe supercomputing systems. Subsequently, the architecture, functions, and performance of common parallel libraries such as grid processing libraries, partial differential equation discrete solving libraries, matrix computing libraries, particle transport libraries, collective communication libraries, and deep learning libraries are highlighted. Finally, a summary of typical application software on Tianhe supercomputers shows that the parallel algorithm libraries can effectively support the rapid development and performance optimization of typical application software.