The study of the lifetime of an organism, devices, etc., is very important in the field of health, biology, and industry. We need a distribution that can model the data with certain characteristics. The lifetime distribution with a decreasing hazard rate has been discussed in the new literature. In this research, a new distribution with a decreasing hazard rate is presented with three parameters that match real data that has no zero observation, namely the Exponential Conway Maxwell Poisson distribution (ECOMP). The ECOMP distribution can be used to model the minimum lifetime of an exponential random variable. In this research, we explain how to construct ECOMP distribution and discuss its properties. The parameter estimation is performed using the maximum likelihood method. The application of earthquake data shows that the ECOMP distribution is more suitable in modeling data than the Exponential Poisson (EP) distribution. © 2021 Author(s).