A clamping device and an elevator system. The clamping device includes: a base having a limiting space and an opening communicating with the limiting space; and a clamping arm assembly, which is arranged at the opening of the base and forms a gap with the opening in a stationary state, the gap being smaller than a size of a clamped part; in which the clamp arm assembly has a first damping force that allows the clamped part to enter the limiting space via the opening, and has a second damping force that allows the clamped part to exit the limiting space via the opening; and the second damping force is greater than the first damping force.