A fan vibration damping structure and a fan with the vibration damping structure. The fan vibration damping structure includes a bearing cup, a first bearing, a second bearing, a third bearing, an elastic member and at least one oil seal. The bearing cup has an internal receiving space and a bearing hole in communication with each other. The first, second and third bearings and the elastic member are disposed in the receiving space. A high-viscosity-coefficient oil is filled in the receiving space. The fan vibration damping structure is applied to the fan to greatly reduce vibration of the fan in operation.