Okasa et al. (Okasha, H. M., Kayid, M., Abouammoh, M. A., and Elbatal, I., “A New Family of Quadratic Hazard Rate Geometric Distributions with Reliability Applications,” J Test. Eval., Vol. 44, No. 5, 2015, JTE20150116 [DOI: 10.1520/JTE20150116] introduced the novel quadratic hazard rate geometric distribution. Here, we introduced a generalization containing Okasha et al.’s distribution as a particular case. The generalization was shown to be more flexible by reanalyzing the real data set in Okasha et al. and another real data set.