In this paper, we apply the differential transform (DT) method for finding approximate solution of the system of linear and nonlinear Volterra integro-differential equations with variable coefficients, especially of higher order. We also obtain an error bound for the approximate solution. Since, in this method the coefficients of Taylor series expansion of solution is obtained by a recurrence relation, thus we can use arbitrary number of Taylor series terms to obtain solutions with desired accuracy. Here we give some preliminary results of the differential transform and show that the DT method can be easily applied to a wide class of linear and nonlinear systems. Finally, the accuracy and simplicity of this method will be verified by solving some examples.