In this article, a new three parameter lifetime model is proposed as a generalisation of the moment exponential distribution. The proposed model is named as Topp-Leone moment exponential distribution. The induction of two additional shape parameters will enhance the capability of the proposed model to handle the complex scenarios in modelling. Several properties of the proposed model are discussed. The model parameters are estimated using method of maximum likelihood. Real life applications of the proposed model have been carried out by using datasets from the fields of botany, archaeology and ecology.