This article introduces the Marshall–Olkin generalized Erlang-truncated exponential (MOGETE) distribution as a generalization of the Erlang-truncated exponential (ETE) distribution. The hazard rate of the new distribution could be increasing, decreasing or constant. Explicit-closed form mathematical expressions of some of the statistical and reliability properties of the new distribution were given and the method of maximum likelihood estimation was used to estimate the model parameters. The usefulness and flexibility of the new distribution was illustrated with two real and uncensored lifetime data-sets. The MOGETE distribution with a smaller goodness of fit statistics always emerged as a better candidate for the data-sets than the ETE, Exp Fréchet and Exp Burr XII distributions.