The invention discloses a resonance-peak-free vibration isolator of an L-shaped resistance arm, and a damping module of the resonance-peak-free vibration isolator. The resonance-peak-free vibration isolator consists of a vibration damping module, the damping module and a connection module, wherein the vibration damping module comprises a hollow internal thread hexagon bolt, an internal thread sleeve and a main spring; the damping module comprises a waist-drum-shaped damping sleeve, a first L-shaped damper, a second L-shaped damper and a damping module buffering spring; and the connection module comprises an upper end cap, a fastening pressure plate, a lower cover cap with a cylindrical bulge, and a base. The damping module disclosed by the invention is simple in implementation structure. When the vibration isolator vertically vibrates, the two L-shaped dampers in the damping module are respectively in contact with two concave ports, so that stable damping force in vertical and horizontal directions can be provided, good centering and resetting effects on transverse vibration can be realized, and the resonance inhibiting effect is good. The damping module disclosed by the invention is simple in implementation structure, and has a good inhibiting effect on transverse resonance and longitudinal resonance.