The invention discloses a variable-damping variable-rigidity viscoelasticity-friction composite damping device. The variable-damping variable-rigidity viscoelasticity-friction composite damping devicecomprises two symmetric cylinder type viscoelasticity damping device units and two cylinder type friction damping device units, the friction damping device units sleeve the outer sides of the cylinder type viscoelasticity damping device units, the cylinder type viscoelasticity damping device units sequentially comprise annular inner steel cylinders, annular viscoelasticity material layers and annular middle steel cylinders from inside to outside, elastic elements are sleeved with the middles of the annular inner steel cylinders, closed steel plates are mounted on two ends of the annular innersteel cylinders, cylinder viscoelasticity materials are mounted on inner sides of two ends of the annular middle steel cylinders, connecting anchorage steel plates are mounted on two ends of the annular middle steel cylinders, the friction damping device units sequentially comprise annular middle steel cylinders, annular friction pieces, annular friction plates and annular outer steel cylinders from inside to outside, the annular friction plates comprise first annular friction plates and second annular friction plates, and each annular outer steel cylinder is formed through connecting of an upper half annular outer steel cylinder and a lower half annular outer steel cylinder through bolt assembling.