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The main objective of this research is to simulate the electrical activity of cardiac tissue by finite element method. Electrical activity is responsible for the periodic contraction and relaxation cycle of the human heart. Mathematical modeling of heart provides a better understanding for the complex biophysical phenomena related to electrical activity in the heart. Various electro-physical models have been developed to simulate electrical properties of cardiac tissue. In this research work monodomain model which is coupled with the single cell FitzHugh-Nagumo model is used to simulation the electrical activities. Two dimensional monodomain model equations on a general domain with equal isotropy and no fiber orientation are considered. Finite element method which has been widely used as an analysis and design tool is used to deal with the complex monodomain model equations. The single cell simulation represents the behavior system by changing the parameters of single cell model.The outcome of the simulation represents the effect of applied current and threshold value on the model behavior