In this paper, we introduce the binomial state of a two-level atomic system, which is a state that yields a binomial probability distribution. Its generation, squeezing, antibunching, and subpoisson statistics are discussed. It reduces to the Glauber coherent state in certain limit, and in that limit, the binomial distribution reduces to the Poisson distribution. This limiting process destroys all nonclassical effects of the system. The Bloch vector model is used to discuss the quantum characters of mixed state of one atom. Finally, the binomial state of the atomic system and the binomial state of the Bose system is compared. It is shown that the binomial state of a Bose system can not be produced in a atomic system.