APTCHA is an important means to improve network security and prevent hackers. Since only a simple transfigure processing and the same style. CAPTCHA are lack of security and have a high rate to be cracked. Hence it is important for network security to design a new method of transfigure having random and complex feature. The paper creates an algorithm using contraction mapping principle and fixed point, with a way of circumvolution and translation. The algorithm randomly select a fixed point in the character picture and make a transfigure using fixed point principle. The experimental results show that the CAPTCHA based on contraction mapping has a strong randomness and difficult to be recognized by computer programs, which can provide a strong security for Web applications.