In this paper, a novel analytical approximation for the period and periodic solutions for the
Helmholtz-Duffing oscillator is presented. The main idea of present work is to approximate the integration
in exact analytical period of equation using a well-known quadrature rules. This approach gives us not only the
accurate period of motion but also a truly periodic solution in a rational form as a function of the amplitude
of oscillation. Comparison of the result obtained using this approach with the exact one and existing results
reveals that the high accurate, simplicity and efficiency of the proposed procedure for the whole range of initial
amplitudes and the equation parameter in a variety of cases. The method can be easily extended to other
strongly nonlinear oscillators.