The effective frequency of nonlinear vibration isolation is generally greater than the jump-down frequency, i.e. the jumping frequency range due to the multiple solutions of the nonlinear dynamic equations is excluded. However, when the oscillation amplitude is on the non-resonance branch of the response curve, the nonlinear isolator is capable of reducing the transmitted force efficiently. How to make the response amplitude be on the non-resonance branch by control strategy is the key for isolator design in the jumping frequency range. In this paper, an optimal time-delay feedback control method is proposed to shift the amplitude from resonance branch to non-resonance branch, when the amplitude is on the resonance branch due to certain initial conditions or variation of excitation frequency against time. Although the control makes system chaotic, the oscillation amplitude is reduced significantly. Furthermore, the control is removed, when the transient response of chaotic vibration dies away and the system state (displacement, velocity) is in the basin approaching to the steady focus, corresponding to the non-resonance branch, in the Von der Pol Plane. After the halt of the control, the system will recover harmonic vibration and the amplitude will be on the non-resonance branch. Consequently, the nonlinear isolator will be active in the jumping frequency range under any conditions by mean of optimal time-delay feedback control. The efficiency of this method is verified by numerical simulations. Comparisons between the nonlinear isolator and the corresponding linear one and discussions on the effects of damping factor are carried out, which shows that the nonlinear isolator, including quasi-zero stiffness springs and optimal time-delay feedback control, is favorable for low frequency isolation.