In this paper, a new lifetime distribution called compounded geometric-mixture exponential distribution is proposed by compounding the mixture exponential and geometric distributions. Some properties of the new distribution such as survival function, hazard function, moments, Lorenz and Bonferroni curves, etc. are obtained. The estimations of four parameters of the new model are studied by several methods. A Monte Carlo simulation study is performed to understand the behavior of estimators. Two real data applications are also provided.