The optimization issue of a nonlinear energy sink （NES） with double springs and harmonic excitation is investigated. The dynamic equation of a linear oscillator （LO） with the NES is established， and the system response is calculated by the Runge-Kutta method. The optimization goal is to minimize the maximum steady-state displacement amplitude of the LO in the frequency domain. The differential evolution algorithm and the parameter analysis method are used to optimize the parameters of the NES， and the optimized results are compared with those of the linear vibration absorber. The results remonstrate that the range of the spring stiffness of the NES can be quite large for decent vibration attenuation effects. The optimal parameter region and frequency response of the NES are greatly influenced by the excitation amplitude.