We introduce a new family of continuous distributions called the odd inverse Pareto-G class which extends the exponentiated-G family due to Gupta et al. [R. C. Gupta, P. L. Gupta, R. D. Gupta, Comm. Statist. Theory Methods, 27 (1998), 887–904] and the Marshall-Olkin-G class due to Marshall and Olkin [A. W. Marshall, I. Olkin, Biometrika, 84 (1997), 641–652]. We define and study two special models of the proposed family which are capable of modeling various shapes of aging and failure criteria. The special models of this family can provide reversed J-shape, symmetric, left skewed, right skewed, unimodal or bimodal shapes for the density function. Some of its mathematical properties are derived. The maximum likelihood method is used to estimate the model parameters. By means of two real data sets we show that the special models of this family have superior performance over several existing distributions.