Nonlinear ordinary differential equations (ODEs) are commonly used for modeling physical, chemical, and biological systems. Mathematical models and their simulations are important for understanding the quality and quantity of these systems. Infectious disease mathematical models are widely used by many researchers. Epidemic models have become a valuable tool for the analysis of dynamics of infectious disease in recent years. Unfortunately, often the analytic solution of such differential equations can not be obtained explicitly . Hence, numerical methods to solve approximately these models. One of the simplest numerical techniques is the finite difference methods. This paper aims to present an efficient numerical method to study the fractional time SIR epidemic model. The numerical method that used to study this model is the nonstandard Grünwald-Letnikov finite difference method. Comparative study with the standard methods is done. Various graphs are presented to describe the numerical results. The obtained results indicate that the proposed method has been successful applied to efficiently study the SIR epidemic model.