The invention discloses an eddy current magnetic resistance hyperboloid friction pendulum support. The eddy current magnetic resistance hyperboloid friction pendulum support is composed of an upper support plate, an upper magnetic conductive plate, an upper eddy current plate, an upper wear-resisting plate, a permanent magnet spherical crown, a lower wear-resisting plate, a lower eddy current plate, a lower magnetic conductive plate and a lower support plate, wherein the permanent magnet spherical crown is composed of an upper friction plate, a permanent magnet, a support unit and a lower friction plate. When the eddy current magnetic resistance hyperboloid friction pendulum support is under the action of horizontal earthquake, the permanent magnet spherical crown moves reciprocatingly between the upper curved wear-resisting plate and the lower curved wear-resisting plate, and according to the principles of electromagnetism, the upper eddy current composite plate and the lower eddy current composite plate reciprocatingly cut off magnetic induction liens to produce eddy current and accordingly to generate magnetic damping, and further the magnetic damping consumes the motion energyof the eddy current magnetic resistance hyperboloid friction pendulum support together with coulomb friction damping produced by the friction plates. The eddy current magnetic resistance hyperboloid friction pendulum support has the advantages of being maintenance-free, low in manufacturing price, good in weather resistance and the like and belongs to the technical field of friction pendulum supports.