The invention discloses a piecewise nonlinear vibration isolator and a design method therefor. The method comprises: firstly, adopting an analytic method, i.e., an average method to obtain an amplitude frequency expression of vibration response of the piecewise nonlinear vibration isolator; secondly, according to the amplitude frequency expression, obtaining a relationship expression of an extreme response value and each parameter of a vibration system, adopting a numerical solution to obtain correct solutions and the number of solutions of the extreme response value, and obtaining a changing rule that the number of extreme response values changes with the parameters of the vibration system; thirdly, analyzing main structural parameters of the piecewise nonlinear vibration isolator, such as an influence of different measurement values of damping ratio and the value of base excitation on a frequency island and a changing rule of the number of the extreme response values, and if the number of the extreme response values is larger than 1, determining that the vibration response possibly causes a frequency island phenomenon, or otherwise, determining that the frequency island phenomenon does not occur; and finally, according to the values of the base excitation and the damping ratio, determining the structural parameters of the segmental nonlinear vibration isolator, so that the segmental nonlinear vibration isolator that avoids the frequency island phenomenon is designed. According to the method, the condition for removing frequency islands can be conveniently obtained; and the method is high in operability.