Following SINGH's [9] characterization of positive-poisson distribution and SHANMUGAM and SINGH'S [8] characterization of logarithmic series distribution, a characterization of the positive-binomial distribution and its goodness-of-fit application are given. Our results are illustrated using PEAKSON's [7] data on the number of albino children in a family. Also, we show that our expressions for the positive-binomial distribution approach in limit SINGH's expressions for the positive-poisson where the positive-poisson is considered as a limiting distribution of the positive-binomial.