We develop and study in detail a new family of distributions called Half-logistic Odd Power Generalized Weibull-G (HLOPGW-G) distribution, which is a linear combination of the exponentiated-G family of distributions. From the special cases considered, the model can fit heavy tailed data and has non-monotonic hazard rate functions. We further assess and demonstrate the performance of this family of distributions via simulation experiments. Real data examples are given to demonstrate the applicability of the proposed model compared to several other existing models.