Graphics processing unit (GPU) has been developing rapidly in recent years at a speed over Moor's law, and as a result, various applications associated with computer graphics advance greatly. At the same time, the highly processing power, parallelism and programmability available nowadays on the contemporary GPU provide an ideal platform on which the general-purpose computation could be made. Starting from an introduction to the development history and the architecture of GPU, the technical fundamentals of GPU are described. Then in the main part of the paper, the development of various applications on general purpose computation on GPU is introduced, and among those applications, fluid dynamics, algebraic computation, database operations, and spectrum analysis are introduced in detail. The experience of our work on fluid dynamics has been also given, and the development of software tools in this area is introduced. Finally, a conclusion is made, and the future development and the new challenge on both hardware and software in this subject are discussed.