The invention provides an internal and external multiple energy-dissipation tension-compression damper, and belongs to the field of building structure vibration control. The damper comprises connection plates, connection plate threaded holes, fixing end plates, a tension-compression energy-dissipation steel plate, connection energy-dissipation steel plates, squeezing energy-dissipation plates, arc-shaped energy-dissipation steel plates, mild steel energy-dissipation internal cylinders, lead dot holes, an energy-dissipation filling material, energy-dissipation ribs, built-in elliptical holes, end plates, lead dots, a cover plate, tension-compression connectors, coordinated connection rebars and locking nuts. The internal and external multiple energy-dissipation tension-compression damper has the advantages that the initial stiffness is high, the steel yielding area is large, the energy-dissipation effect is good, the structural design of internal and external combined energy dissipationis adopted, multiple energy-dissipation effects are achieved, and energy is more sufficiently dissipated; moreover, the internal and external multiple energy-dissipation tension-compression damper has a reasonable initial stiffness, and can meet the requirements for supporting and bearing of the damper while shock absorption and energy dissipation are achieved.