A new generalization of the Poisson distribution, with two parameters λ1and λ2, is obtained as a limiting form of the generalized negative binomial distribution. The variance of the distribution is greater than, equal to or smaller than the mean according as λ2is positive, zero or negative. The distribution gives a very close fit to supposedly binomial, Poisson and negative-binomial data and provides with a model suitable to most unimodel or reverse J-shaped distributions. Diagrams showing the variations in the form of the distribution for different values of λ1and λ2are given.