In this paper we introduce a new three parameter distribution called the generalized odd log-logistic exponential (GOLLEx) distribution. The proposed distribution possesses a very flexible hazard rate function shapes which provide a more flexibility in data analysis. We study the main properties of the proposed distribution including quantiles, moments, moment generating function. We obtain the maximum likelihood and Bayes estimates of the GOLLEx distribution based on complete and type-II censored data. The Bayes estimates of the unknown parameters are obtained by using the Markov Chain Mont Carlo (MCMC) approach under the assumption of the independent gamma priors. We perform a simulation study to compare the performance of the different estimators. Finally, we analyze a real data set under the complete sample case to show the applicability of the proposed estimates.