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To study the heterogeneous nature of lifetimes of certain mechanical or engineering processes, a mixture model of some suitable lifetime distributions may be more appropriate and appealing as compared to simple models. This paper considers mixture of Topp-Leone distributions under classical and Bayesian perspective based on complete sample. The new distribution which exhibits decreasing and upside down bathtub shaped density while the distribution has the ability to model lifetime data with decreasing, increasing and upside down bathtub shaped failure rates. We derive several properties of the new distribution such as moments, moment generating function, conditional moment, mean deviation, Bonferroni and Lorenz curves and the order statistics of the proposed distribution. Moreover, we estimate the parameters of the model by using frequentist and Bayesian approaches. For Bayesian analysis, five loss functions, namely the squared error loss function (SELF), weighted squared error loss function (WSELF), modified squared error loss function (MSELF), precautionary loss function (PLF), and K-loss function (KLF) and uniform as well as gamma priors are considered to obtain the Bayes estimators and posterior risk of the unknown parameters of the model. Furthermore, credible intervals (CIs) and highest posterior density (HPD) intervals are also obtained. Monte Carlo simulation study is done to access the behavior of these estimators. For the illustrative purposes, a real-life application of the proposed distribution to a tensile strength data set is provided. [ABSTRACT FROM AUTHOR]