In this paper, we construct a backward difference scheme for a class of SIR epidemic model with general incidence f . The step sizeτ used in our discretization is one. The dynamical properties are investigated (positivity and the boundedness of solution). By constructing the Lyapunov function, the general incidence function f must satisfy certain assumptions, under which, we establish the global stability of endemic equilibrium when R₀ >1. The global stability of diseases-free equilibrium is also established when R₀ ≤1. In addition we present numerical results of the continuous and discrete model of the different class according to the value of basic reproduction number R₀.