According to quantum mechanics, quantum state has many advantages of the coherence and entanglement and the inner parallelism of quantum algorithm is totally different from the classical algorithm. Shor's algorithm shows the advantage of quantum algorithm in solving some classical Non-polynomial problems, then Grover's search algorithm further proves this point. And this brought more and more research on quantum algorithm in many countries and they have got great achievements especially on quantum intelligent algorithm. In this paper, the development and fundamental principles of quantum computing are generalized, then three typical quantum algorithms is introduced, and the superiority of quantum computer is explained. Finally, current research of quantum computation are introduced.