A new generalization of the Dagum distribution called the Marshall-Olkin Dagum distribution is proposed and studied. The hazard rate function of the new model can be increasing, decreasing, decreasing-increasing-decreasing, bathtub, unimodal or biomodal shaped. Many mathematical properties of this distribution including quantile function, ordinary and incomplete moments, Bonferroni and Lorenz curves, mean residual life, mean waiting time, order statistics and probability weighted moments are derived. The method of maximum likelihood is used for estimating the model parameters. The flexibility of the proposed model is illustrated by an application to real data.