This paper proposes a new four-parameter distribution called the odd Lindley Burr XII (OLBXII) distribution. The hazard rate function of the OLBXII distribution can be constant, increasing, decreasing, unimodal or bathtub shape. A comprehensive account of some of its mathematical properties are derived. The density function of the proposed model can be expressed as a linear combination of Burr XII densities. The esimation of the model parameters is carid out using the maximum likelihood method. The importance and flexibility of the proposed model are proved empirically using two real data sets.