In recent years, there are many efforts to develop new statistical distribution with more flexibility which can be fitted well to complex data. In this paper we develop a compounded distribution of two-parameter inverse Weibull with geometric random variables, so-called the exponentiated inverse Weibull geometric (EIWG) distribution. We study the properties of the EIWG distribution such as moments, moment generating function, mean deviations, Bonferroni and Lorenz curves, entropies and order statistics, and obtain the maximum likelihood estimations of the parameter of the distribution using EM algorithm and Bayesian estimations using Gibbs sampler. Finally, the EIWG distribution is applied to model a simulated and real failure data, with appropriate model comparison with the competing models.