A new distribution called Ristić and Balakrishnan Lindley-Poisson (RBLP) distribution is introduced and its properties are explored. This new distribution contains several new and well known sub-models, including Lindley-Poisson, RB-Lindley and Lindley distributions. Some statistical properties of the proposed distribution including hazard rate function, moments and conditional moments are presented. Mean deviations, Lorenz and Bonferroni curves, Rényi entropy and distribution of the order statistics are given. Maximum likelihood estimation technique is used to estimate the model parameters. Finally, application of the model to a real dataset is presented to illustrate the usefulness of the proposed distribution.