Abstract: A shock absorbing adjusting structure includes a cylinder with a tube movably received in the cylinder. One end of the cylinder is connected to a part of a bicycle frame and one end of the tube is connected to another part of the bicycle frame. A sleeve is fixedly connected to the cylinder and connected to a piston assembly movably inserted in the sleeve. A tapered hole and a plurality of through holes are defined through the piston assembly. A seal member is urged by a spring in the piston assembly and seals the through holes. A pusher in the piston assembly is urged by a rod which extends from an inside of the cylinder and is movably received in the sleeve. The rod is moved by an actuating bar which is operated by a rider from outside of the cylinder so as to movably adjust a tapered tip of the rod relative to the tapered hole in the piston assembly.