A new generalization of the exponentiated half-logistic-G distribution is developed to produce a new family of distributions referred to as the Marshall-Olkin-exponentiated half logistic-G distribution. The new family of distributions is an infinite linear combination of the exponentiated-G family of distributions. We considered some special cases of the new distribution and we conclude that the distribution can handle heavy tailed data and non-monotonic hazard rate functions. A simulation study was conducted to assess the consistency of the maximum likelihood estimates. Real data examples are provided to demonstrate the usefulness of the proposed model in comparison with other competing models.