the ConwayMaxwellPoisson distribution is a useful discrete distribution, this distribution is a twoparameter extension of the Poisson distribution. Its statistical and probabilistic properties are researched and explored. Taking the moment generating function as a tool, the digital features and moment of the distribution are discussed, the implicit equations about the point estimates of parameters are given, the Fisher information matrix about parameters is derived. Finally we study the conjugate distribution about parameters, the marginal distributions of the conjugate distribution and conditional distributions.