Summary: ``In this paper, we deal with an SIQR epidemic model with isolation and nonlinear incidence rate. We have obtained a threshold value $\scr R_0$ and shown that there is only a disease free equilibrium point when $\scr R_0<1$, and there is also an endemic equilibrium point if $\scr R_0>1$. With the help of Lyapunov function, we have obtained some results about the global stability of disease free- and endemic equilibrium points, which are applicable for non-monotone, non-concave incidence rate.''