Abstract: In this study, an optimized explicit Runge-Kutta (RK) method which is based on a method of Dormand with six-stage and fifth algebraic order with FSAL property denoted as the ORK5 method is constructed. The proposed method solves first-order Ordinary Differential Equations (ODEs) by first converting the second order ODEs to an equivalent first order. The new method has zero phase-lag, zero amplification error and zero first derivative of the phase-lag. Absolute stability of the new method is as well shown. The numerical experiments are carried out to show the efficiency of the derived method in comparison with other existing RK methods.