High performance computing has opened the door to using bioinformatics and systems biology to explore complex relationships among data, and created the opportunity to tackle very large and involved simulations of biological systems. Many supercomputing centers have jumped on the bandwagon because the opportunities for significant impact in this field is infinite. Development of new algorithms, especially parallel algorithms and software to mine new biological information and to assess different relationships among the members of a large biological data set, is becoming very important. This article presents our work on the design and development of parallel algorithms and software to solve some important open problems arising from bioinformatics, such as structure alignment of RNA sequences, finding new genes, alternative splicing, gene expression clustering and so on. In order to make these parallel software available to a wide audience, the grid computing service interfaces to these software have been deployed in China National Grid (CNGrid). Finally, conclusions and some future research directions are presented.