The invention provides a vibration isolator based on rhomboid periodic structures. According to the vibration isolator based on the rhomboid periodic structures, the middle position between one up anddown plate at the upper portion and one up and down plate at the lower portion is provided with a viscous elastic damping square block, concave platforms A of the up and down plate at the lower portion are internally provided with bosses B at the lower portions of four sets of double-diamond elements, the concave platforms A of the up and down plate at the upper portion are internally provided with the bosses B at the upper portions of the four sets of double-diamond elements, the up and down plate at the upper portion is connected with machinery equipment through bolt holes C, the up and down plate at the lower portion is connected with the base ground through the bolt holes C, the upper portions of small diamond elements inside corresponding large diamond elements are connected with theupper portions of the corresponding large diamond elements through first vertical beams, the lower portions of the small diamond elements inside the corresponding large diamond elements are connectedwith the lower portions of the corresponding large diamond elements through second vertical beams, and the upper portions and the lower portions of the large diamond elements are provided with the bosses B correspondingly. The vibration isolator based on the rhomboid periodic structures is lightweight and simple and compact in structure, and the designed vibration isolator is convenient to install, high in static rigidity and good in vibration reduction effect, contains damping vibration reduction, is of optimization design and adjustable rigidity and is applied in the technical field of rotating machinery foundation vibration reduction.