A triple-folding umbrella skeleton includes a plurality sets of frame arranged around the middle tube and pivotably mounted on the notch and runner respectively. Each frame set includes a first rib, a second rib, a third rib, a stretcher and a first link. One end of the first rib is pivotably mounted on the runner. The two ends of the second rib is pivotably mounted to the other end of the first rib and one end of the third rib respectively. One end of the stretcher is pivotably mounted on the notch, and other end of the stretcher is pivotably mounted to the first rib. The first link is generally parallel to the first rib, and its two ends is pivotably mounted to a first extension portion of the second rib and the stretcher respectively. The first link, the stretcher, the first rib and the first extension portion cooperate to form a quadric link structure. The triple-forming umbrella skeleton is characterized in that each frame set further includes a connecting spring and a second link generally parallel to the second rib. One end of the second link is pivotably mounted to a second extension portion of the third rib, and the other end of the second link is connected to the first rib via the connecting spring. Whereby, each frame set can be expanded to a largest extent to obtain a largest canopy shielding area, and only a smaller force is needed to open the triple-folding umbrella skeleton, due to the retractability of the connecting spring.