In this paper, we introduce a new five-parameter distribution with increas-ing, decreasing, bathtub-shaped failure rate called the Beta-Weibull-Logarithmic (BWL) distribution. Using the Sterling Polynomials, various properties of the new distribu-tion such as its probability density function, its reliability and failure rate functions, quantiles and moments, Renyi and Shannon entropies, moments of order statistics, Bonferroni and Lorenz curves were derived. then the maximum likelihood estimation of BWL distribution for the parameters of BWL distribution are found. Finally the usefulness of this distribution for real data are presented.