In this paper, a new flexible extension of the log-logistic model called the extended odd Weibull log-logistic (EOWLL) distribution is studied. The EOWLL density can be expressed as a mixture of Dagum densities. The EOWLL distribution provides decreasing, increasing, upside-down bathtub, and reversed-J-shaped hazard rates, and right-skewed, symmetrical, and left-skewed densities. Its mathematical properties are derived. The EOWLL parameters are estimated via eight classical methods of estimation. Additionally, extensive simulations are obtained to explore the performance of the proposed methods for small and large samples. Two real-life sets of data from medicine and geology are analyzed, showing the flexibility of the EOWLL distribution as compared to other log-logistic extensions. The results show that the EOWLL distribution is more appropriate as compared to the Kumaraswamy transmuted log-logistic, alpha-power transformed log-logistic, and additive Weibull log-logistic distributions, among others.