A new discrete distribution involving geometric and discrete Pareto as special cases is introduced. The distribution possesses many interesting properties like decreasing hazard rate, zero vertex uni-modality, over-dispersion, infinite divisibility and compound Poisson representation, which makes the proposed distribution well suited for count data modeling. Other issues including closure property under minima, comparison of its distribution tail with other distributions via actuarial indices are discussed. The method of proportion and maximum likelihood method are presented for parameter estimation. Finally the performance of the proposed distribution over other classical and newly proposed infinitely divisible distributions are discussed.