Abstract: In this paper the general concept of Poisson-size-biased Lindley (PSBL) distribution is presented. Its p.m.f. is obtained. Some of its properties and the expressions for raw and central moments, coefficients of skewness and kurtosis are derived. The moment equations and the maximum likelihood estimators of the parameter of this Poisson size-biased Lindley (PSBL) distribution have been obtained for estimation its parameters. A simulation of a parameter is study has been proposed.