In this paper, a quasi-zero stiffness (QZS) clamping mechanism based on beams is proposed for constant-force support and vibration isolation at low frequency. The QZS property is realized by combining the inclined beams with negative stiffness and the circular arches with positive stiffness. Mechanical model of the mechanism is derived theoretically, and a parameter design based on Taguchi method is carried out, leading to the mechanism with ultra-low stiffness. After that, static characteristic of the mechanism is simulated and is approximately consistent with the theoretical results. On this basis, the dynamic behavior of vibration control is analyzed to study the vibration isolation performance. Simulation results show that the proposed mechanism can provide constant preload force (about 5.2 N) and have better vibration isolation performance at low frequency.