In this paper, the discrete Erlang-truncated exponential distribution is defined by using the general approach of discretizing a continuous distribution while retaining its survival function. The statistical properties of the discrete Erlang-truncated exponential distribution such as the quantile function, moments, moment generating function, Rényi entropy and order statistics are calculated. The estimation of the parameters of the model is approached by the maximum likelihood (ML) method. The stressstrength parameter is obtained and estimated by using ML method.