A new generalization of negative Polya-Eggenberger distribution (GNPED) has been obtained by mixing the negative binomial distribution with generalized beta distribution-Π defined by Nadarajah and Kotz (2003). Some special cases and properties of GNPED have been studied. Further, the proposed model has been fitted to two data sets (used by Gupta & Ong, 2004) that provide a satisfactory fit and better alternative as compared to negative binomial and some of its mixture models and extensions. Also, the negative Polya-Eggenberger distribution (NPED), obtained by mixing negative binomial with beta distribution of I-kind, has been fitted to the same data sets for comparison.