Chaotic maps with its characteristic are very useful in cryptography, however, compared with wide application in symmetric system, the research about chaos in public-key encryption system is still few. Through analysing the period of toms automorphisms which is a prototype of chaotic map, and making use of the framework of the traditional public-key algorithm RSA, the authors propose a chaotic public-key encryption algorithm based on toms automorphisms. Its security is based on the intractability of the integer factorization problem as RSA, and it is able to resist the chosen-ciphertext attack against RSA and easy to be implemented.