Geometric stable distributions are the weak limits of appropriately normalized geometric random sums of independent and identically distributed random variables.These classes of distributions have wide variety of applications especially in the field of reliability, biology, economics, insurance mathematics etc. Asymmetric Laplace distribution plays an analogues role among geometric stable laws as Gaussian distributions do among the stable laws. Purdom and Holmes (2004) and Juliã and Vives-Rego (2005) discussed the application of the asymmetric Laplace distribution in different fields of medical science and established that it is a good fit for gene expression data and gram-negative bacterial axenic cultures. The purpose of this paper is to develop an autoregressive process that can be used for modelling asymmetric peaked observations.