Traditional vibration isolation of satellite instruments has an inherent limitation that low-frequency vibration suppression leads to structural instability. This paper explores a parallel-coupled quasi-zero stiffness (QZS) vibration isolator for an axially loaded beam, with the goal of enhancing the effectiveness of low-frequency isolation. A QZS contains two magnetic rings, which contribute negative stiffness, and one spiral spring, with positive stiffness, a combination that has high static stiffness to resolve the structural instability. The frequency response functions (FRFs) of power flow are used to measure the effectiveness of vibration isolation. The magnetic stiffness of the magnetic rings is calculated using the principle of equivalent magnetic charge. The heights, radii, and gap of the magnetic rings affect its stiffness. The parallel-coupled QZS vibration isolator of an axially loaded beam is modeled using an energy method. Based on the Galerkin truncation, harmonic balance analysis, and arc-length continuation, an approach is proposed to analyze the FRFs of power flow for the parallel-coupled QZS vibration isolation of an axially loaded beam. Numerical results support the analytical results. Both analytical and numerical results show that the power reduction of axially loaded beams with a parallel-coupled quasi-zero vibration isolation system is more significantly suppressed at low frequencies.