The invention relates to a radial spring type harmonic-peak-free vibration isolator. The radial spring type harmonic-peak-free vibration isolator comprises a base, a hexagonal bolt, an upper end cover, a lower end cover, a vertical damping spring, an internal thread sleeve, a damping sleeve and a gasket, wherein the lower end cover, the vertical damping spring, the internal thread sleeve, the damping sleeve and the gasket are all arranged in the base. Each radial damping module comprises a radial damping spring, a damping fixed block and a damping movable block. The outer wall of each damping fixed block is in contact with the inner wall of the base. One end of each radial damping spring is connected to the corresponding damping fixed block, and the other end of each radial damping spring is connected to the corresponding damping movable block. The inner side wall of each damping movable block is an arc surface and is in contact with the outer wall of the damping sleeve. Each damping movable block comprises an upper damping movable block body and a lower damping movable block body which are in contact with each other. A movable clearance exists between each upper damping movable block body and the corresponding damping fixed block, and a movable clearance exists between each lower damping movable block body and the corresponding damping fixed block. The radial spring type harmonic-peak-free vibration isolator can achieve better strong impact resisting and vibration isolating effects and belongs to the technical field of vibration isolators.