A new lifetime model called the odd exponentiated half-logistic Burr XII distribution is defined and studied. Its density function can be expressed as a linear mixture of Burr XII densities. The proposed model is capable of modeling various shapes of hazard rate including decreasing, increasing, decreasingincreasing-constant, reversed J-shape, J-shape, unimodal or bathtub shapes. Various of its structural properties are investigated. The maximum likelihood method is adopted to estimate the model parameters. The flexibility of the new model is proved empirically using two real data sets. It can serve as an alternative model to other lifetime distributions in the existing literature for modeling positive real data in many areas.