A method for analyzing steady state vibration of a system with localized nonlinear springs by convolution integral is proposed. Scale of the nonlinear problem can be reduced by using localization of the nonlinear springs in the method. First, equation of motion with the convolution integral of nonlinear restoring force which is treated as an external force is made, second, a set of nonlinear algebraic equations on discrete-time history of unit period is derived and finally the nonlinear algebraic equations is solved with the harmonic balance method. Stable and unstable condition of the steady state vibration can be distinguished by the present method and the impulse response required can be also measured in the experiment because of the merit of the convolution integral. Two examples are shown and the validity of the method is discussed in comparison with Runge-Kutta-Gill method or the experiment.