A friction-damping energy absorber has two ends, at least one core post, two supporting boards, multiple first material layers, and multiple second material layers. The at least one core post has multiple sliding sheets stacked with each other. The two supporting boards are mounted on the ends of the friction-damping energy absorber. The first material layers and second material layers are alternately mounted between the two supporting boards and surround the at least one core post to enable the first material layers and the second material layers to alternately mount with at least one of the sliding sheets of the at least one core post. The friction-damping energy absorber can be used on buildings, bridges, large objects or equipments to absorb and isolate the three-directional vibration energy of earthquakes and environments, and can prevent the operation temperature from increasing and provide an automatic adjustment function of damping and stiffness.