The invention belongs to the field of robots, and relates to a finger transmission device of a multi-joint robot. The finger transmission device comprises a first knuckle, a second knuckle, a third knuckle, a reset spring I, a reset spring II, a reset spring III, a springback rope I, a springback rope II, a springback rope III, a tension rope I, a tension rope II, a tension rope III, a motor output tray I, a motor output tray II and a motor output tray III. According to the finger transmission device, springback rope and tension rope mounting grooves are additionally formed in the three knuckles, so that the three springback ropes and the three tension ropes are positioned in the three knuckles and are completely limited. The three reset springs are arranged, so that the pull direction of the three reset springs is collinear with the movement direction of the three springback ropes. By adopting the principle, the three springback ropes cannot be loose. The idle stroke of a motor does not exist when robot fingers are controlled to bend and straighten. The three springback ropes and the three tension ropes are respectively used for controlling the three knuckles, so that a robot finger structure is operated in various manners.