Abstract In this project we model the transmission dynamics of Hepatitis B using SLICRV model. Hepatitis B is a potentially life threatening liver infection caused by the Hepatitis B Virus (HBV) and is a major global health problem. HBV is the most common and serious viral infection. We present characteristics of HBV transmission in the form of a mathematical model. The model has two equilibrium points: the disease free equilibrium and the endemic equilibrium points. The stability condition of each equilibrium point is discussed and has been found to be stable and unstable. Based on the basic reproduction number we can predict the future course of the epidemics and determine the stability of equilibrium points. The disease free equilibrium is asymptotically stable if , in this case the disease dies out (the transmission rate was reduced or recovery rate increased), and endemic equilibrium is asymptotically stable if , in this case the disease will spread (the transmission rate was increased or the recovery rate reduced). A combination of increased vaccination of newborns and immunization of susceptible adults appears to reduce HB prevalence. Numerical techniques have been carried out to solve the system of ordinary differential equations which are obtained in the process of modeling. These solutions show the behavior of the populations in time and the stability of disease free and endemic equilibrium points.