This paper deals with a new two-parameter lifetime distribution with increasing, decreasing and constant hazard rate. This distribution allows the occurrence of zero values and involves the exponential, linear exponential and other combinations of Weibull distributions as submodels. Many statistical properties of the distribution are derived. Maximum likelihood estimation of the parameters is investigated with a simulation study for performance of the estimators. Two real data sets are analyzed for illustrative purposes and it is noted that the distribution is a highly alternative to the gamma, Weibull, Lognormal and exponentiated exponential distributions.