The invention relates to a variable-stiffness spherical magnetic damper. The variable-stiffness spherical magnetic damper comprises a base, an outer cylinder, a first permanent magnet layer assembly and a second permanent magnet layer assembly, wherein the first permanent magnet layer assembly comprises a first aluminum disk, a plurality of first layer spherical permanent magnets, and a first rubber disk cover; the first aluminum disk and two hemispherical first grooves corresponding to the first rubber disk cover form a first accommodating groove corresponding to the first layer spherical permanent magnet; the second permanent magnet layer assembly comprises a guide rod, a second aluminum disk, a plurality of second layer spherical permanent magnets and a second rubber disk cover, wherein the second aluminum disk and two second grooves corresponding to the second rubber disk cover form a second accommodating groove corresponding to the second layer spherical permanent magnet; the guide rod comprises a rod body part and a disc part; a circular hole is formed in the end surface of the outer cylinder; the rod body part is arranged in the circular hole in a movable manner; and the base and the outer cylinder are fixed together in a detachable manner. According to the variable-stiffness spherical magnetic damper disclosed by the invention, the stiffness value of the magnetic damper can be continuously adjusted within a certain range, and the magnetic damper is simple in structure and flexible to use.