Abstract: In this paper, the second order Lagrange interpolation polynomial is introduced into the discretized time domain to represent unknown displacement function in dynamic equilibrium equation. As a result, the unknown velocity and acceleration response functions are expressed in terms of the displacement function and an explicit numerical integration scheme is developed for the dynamic response analysis of structural system with damping. The accuracy and stability of the present scheme are studied and compared with other explicit numerical schemes. It is shown that the present scheme is of second-order accuracy and more efficient than other explicit schemes.