eng Science and Education Publishing American Journal of Applied Mathematics and Statistics 2328-7292 2015-09-20 3 5 184 189 10.12691/ajams-3-5-2 AJAMS2015352 article Basel M. Al-Eideh basel@cba.edu.kw 1 Department of Quantitative Methods and Information System, Kuwait University, College of Business Administration, Safat, Kuwait Today, the the development of a mathematical models for population growth of great importance in many fields. The growth and decline of real populations can in many cases be well approximated by the solutions of a stochastic differential equations. However, there are many solutions in which the essentially random nature of population growth should be taken into account. In this paper, we approximating the moments of the first - passage time for the birth and death diffusion process with immigration to a moving linear barriers. This was done by approximating the differential equations by an equivalent difference equations. A simulation study is considered and applied to some values of parameters which showed the capability of the technique. http://pubs.sciepub.com/ajams/3/5/2/ajams-3-5-2.pdf first passage time birth-death diffusion process immigration difference equations