In this paper, the efficient multi-step differential transform method (EMsDTM) is applied to get the accurate approximate solutions for strongly nonlinear duffing oscillator. The main improvement of EMsDTM which is to reduce the number of arithmetic operations, is thoroughly investigated and compared with the classic multi-step differential transform method (MsDTM). To illustrate the applicability and accuracy of the new method, six case studies of the free undamped and forced damped conditions are considered. The periodic response curves of both MsDTM and EMsDTM methods are obtained and contrasted with the exact solution or the numerical solution of Runge Kutta 4th order (RK4) method. This approach can be easily extended to other nonlinear systems and therefore is widely applicable in engineering and other sciences.