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Recently, it is a research hot spot to apply some chaos map in cryptosystem. Several chaos public-key cryptosystems are proposed, but proven as insecure or inpractical. By analysising the characteristics of Chebyshev polynomials, a public-key cryptosystem has been proposed in the paper. Firstly, the feature of semi group of Chebyshev polynomials is given, modular computation is introduced and the definitive range of Chebyshev polynomials is extended from [-1,1] to real field. Secondly, a new one-way dropdoor function ,which is based on extended Chebyshev polynonials, is established. Then,we propose the correspondent public-key cryptosystem. In the end, it is proven that our algorithms are practical and feasible.