The aim of this note is to introduce new AR(1) model with marginal Lindley ditsribution. It will be shown that distribution of the innovation sequence is mixture of the singular and absolute continuous distribution. Many statistical properties are  derived such as: spectral density, some multi-step ahead conditional measures, run probabilities, stationary solution, uniqueness and ergodicity. The parameters are estimated using three different techniques, and their asymptotic distribution is examined. Some applications of the process are discussed to two real data sets and it is shown that the LAR(1) model fits better than other known non-Gaussian AR(1) models.