Shmueli et al. (2005) have generalized Conway and Maxwell (1962) one-parameter Poisson distribution to a two parameter distribution called Conway-Maxwell-Poisson (CMP) distribution, discussed some of its properties and have fitted the CMP distribution to non-Poisson count data. In this paper, we have found a natural extension of twoparameter CMP to three-parameter distribution, which may be called Conway-MaxwellHyper-Poisson distribution (CMHP). We have discussed some additional moment properties. Using the property of proportionality of probabilities, we characterize CMHP and other special distributions.