This paper developed a quasi zero stiffness (QZS) isolator with a rhombus structure and repulsive permanent magnets, which is systematically studied for large amplitude vibration isolation. The rhombus structure consists of four rods with same length and a linear spring. Statics analysis reveals that the rhombus structure large deformation recovery ability and negative stiffness in large stroke range. Repulsive magnets are introduced to compensate for the negative stiffness of the rhombus structure. Therefore, QZS can be realized in a wide displacement range for a better isolation performance in large amplitude vibration isolation. The theoretical model is established and the derived transmissibility shows that the proposed QZS isolator have low resonant frequency and can effectively suppress the vibration in a wide frequency band. Comparing with the conventional QZS isolator, the isolator using rhombus structure and magnets possesses weak nonlinearity and can avoid stability problem, such as frequency jumping, chaos or bifurcation. A prototype is manufactured and tested verify its advantages in suppressing low frequency and large amplitude vibration. This novel QZS isolator provided a potential approach to passive vibration control of large amplitude vibration.