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This paper proposes a quasi-zero stiffness (QZS) isolator composed of a curved beam (as spider foot) and a linear spring (as spider muscle) inspired by the precise capturing ability of spiders in vibrating environments. The curved beam is simplified as an inclined horizontal spring, and a static analysis is carried out to explore the effects of different structural parameters on the stiffness performance of the QZS isolator. The finite element simulation analysis verifies that the QZS isolator can significantly reduce the first-order natural frequency under the load in the QZS region. The harmonic balance method (HBM) is used to explore the effects of the excitation amplitude, damping ratio, and stiffness coefficient on the system's amplitude-frequency response and transmissibility performance, and the accuracy of the analytical results is verified by the fourth-order Runge-Kutta integral method (RK-4). The experimental data of the QZS isolator prototype are fitted to a nine-degree polynomial, and the RK-4 can theoretically predict the experimental results. The experimental results show that the QZS isolator has a lower initial isolation frequency and a wider isolation frequency bandwidth than the equivalent linear isolator. The frequency sweep test of prototypes with different harmonic excitation amplitudes shows that the initial isolation frequency of the QZS isolator is 3 Hz, and it can isolate 90% of the excitation signal at 7 Hz. The proposed biomimetic spider-like QZS isolator has high application prospects and can provide a reference for optimizing low-frequency or ultra-low-frequency isolators. [ABSTRACT FROM AUTHOR]