Cirrhosis of liver has become life-threatening for the human being all over the world. It is the result of long-term continuous damages of the liver. In this paper, we have developed a compartmental model of liver cirrhosis to study the dynamics behavior of this chronic disease. We have formulated the model in terms of a set of nonlinear ordinary differential equations (ODEs), based on the characteristics of disease transmission. The aim of this study is to take a close look at the transmission dynamics of liver cirrhosis. The model is developed with the focus on the concentration of the basic reproduction number and related stability analysis for the disease-free and endemic equilibrium points. Finally, Numerical simulations have been performed to illustrate the disease behavior. Our analysis reveals that infected and liver cirrhotic individuals continue to grow up and the recovered individuals start to decrease as the disease transmission rate and acute infection rate increase. As a result, the disease becomes progressive.