Due to its simple structure and good deployable characteristics, scissor-like structure (SLS) is widely used in many fields, such as mechanical engineering, structure engineering, and aerospace engineering. Because of its inherent structural characteristics, a SLS can possess superior nonlinearities both in equivalent stiffness and damping only with linear component. It also has high loading capacity and excellent equilibrium stability. Thus, it is promising as a vibration isolator. Based on recent findings, a theoretical study is herein executed to build up a universal stiffness model of full types of SLS (including 6 assembly types), considering mass of scissor arm, Coulomb and viscous friction forces in joint parts. Plus more, perturbation method (PM) and average method (AM) are applied to investigate vibration isolation performances of SLS with different assembly types and installation parameters and to compare them with known quasi-zero-stiffness vibration isolators in the literature. Finally, a simulation is done to testify the presented findings and to compare them with former studies. It is shown that: without changing its overall structure and outside dimensions, a SLS vibration isolator can have significantly different nonlinear stiffness for specific nonlinear characteristics only through adjusting assembly type, installation parameters, and initial deformation of its linear component. Since allowable workspace of a vibration isolator is always limited by isolation object and its surrounding structure, this finding indicates a new way to design and modify vibration isolation performance of a system. It will greatly expand application of SLS in vibration isolation.