This paper presents a study of a quasi-zero-stiffness (QZS) isolator. A unique relationship between the geometry configuration and the stiffness of the spring elements is obtained in order to design the property of high-static-low-dynamic stiffness. Analytical solutions of the nonlinear QZS system are derived with the harmonic balance method for the characteristic analysis of the force transmissibility and critical conditions for occurring jump-down and jump-up phenomena. The effects of damping and excitation force on the system behaviors are discussed. A series of experimental tests demonstrate that the QZS system greatly outperforms a corresponding linear isolation system. The former enables vibration to be attenuated at 0.5 Hz, while the latter can only execute attenuation after 4.2 Hz. The QZS system is especially effective for vibration isolation in the low-frequency range.