A difference equation is an equation that contains a difference in one or more than one variable. It has significant applications in the mathematical models of the applications of engineering and science. In this paper, we proposed a method for solving ordinary difference equations using discrete Sumudu transform. Some properties of the discrete Sumudu transform have been introduced. The implementations for the test examples of initial value problems of difference equations examined the efficiency of the proposed method. The approximated solutions of initial value problems of ordinary difference equations in discrete domain with different orders have been evaluated and compared with exact solutions of these problems