In order to meet the requirements of electro-optic payload on vibration isolation performance, a high static stiffness and low dynamic stiffness nonlinear vibration isolator with rhombus linkage mechanism as negative stiffness component (rhombus HSLDS vibration isolator) was proposed. The mathematical model of vibration isolator was established by statics analysis method, and stiffness parameter setting and nonlinear adjustment methods were studied; the harmonic balance method (HBM) was used to solve the kinetic equation, and influence of parameters on the vibration isolation performance was analyzed; the theoretical model and conclusions were verified by kinetic simulation software ADAMS and prototype. The test results show that the rhombus HSLDS vibration isolator has convenient parameter adjustment capability, and the zero-position stiffness and stiffness nonlinearity can be set and optimized by parameters of tension spring and linkage. And the optimization effect of vibration isolation caused by stiffness nonlinearity is affected by the damping of main vibration isolator and zero-position stiffness parameter. Compared with traditional linear vibration isolator, the rhombus HSLDS vibration isolator has significant advantage of nonlinear vibration isolation and can better meet the needs of electro-optic payload vibration isolation requirements.