In this paper, the differential transformation method is modified to be easily employed to solve wide kinds of nonlinear initial-value problems. In this approach, the nonlinear term is replaced by its Adomian polynomials for the index k, and hence the dependent variable components are replaced in the recurrence relation by their corresponding differential transform components of the same index. Thus the nonlinear initial-value problem can be easily solved with less computational effort. New theorems for product and integrals of nonlinear functions are introduced. In order to show the power and effectiveness of the present modified method and to illustrate the pertinent features of related theorems, several numerical examples with different types of nonlinearities are considered.