The current research deals with application of a new analytical technique called Energy Balance Method (EBM) for a nonlinear problem. Energy Balance Method is used to obtain the analytical solution for nonlinear vibration behavior of Euler-Bernoulli beams subjected to axial loads. Analytical expressions for geometrically nonlinear vibration of beams are provided. The effect of vibration amplitude on the nonlinear frequency is discussed. Comparison between Energy Balance Method results and those available in literature demonstrates the accuracy of this method. In Energy Balance Method contrary to the conventional methods, only one iteration leads to high accuracy of the solutions which are valid for a wide range of vibration amplitudes.