This paper introduces a new lifetime distribution, so called odd log-logistic exponentiated Weibull distribution. The new distribution has the advantage of being capable of modelling various shapes of aging and failure criteria. We derive various of its structural properties including ordinary and incomplete moments, quantile and generating functions and order statistics. The new density function can be expressed as a linear mixture of exponentiated Weibull densities. We propose a log-linear regression model using a new distribution, the log-odd log-logistic exponentiated Weibull distribution. The maximum likelihood method is used to estimate the model parameters. Simulation results to assess the performance of the maximum likelihood estimation are discussed. We prove empirically the importance and flexibility of the new model by modelling four real datasets.