A passive aligning strategy for the assembly task of a ribbon cable is presented using a sliding surface gripper. Once the gripper grasps the ribbon cable, the sliding surface of the gripper pulls the cable in one direction, and at the end of the pulling process, the box-shaped structure of the fingertip of the gripper passively aligns the cable to a predictable pose. The relationship between the alignment speed of the cable on the sliding surface and the grasping force was modeled and verified by experiments. The maximum position error of the ribbon cable connector aligned by the proposed method was 0.7 mm, which was smaller than the mating tolerance between typical male-and-female connectors. The mating of the connectors was successfully conducted with an industrial robot (ABB IRB120) whose repeatability is less than a millimeter. The entire assembly process of ribbon cable connectors, including visual recognition of the ribbon cable pose, grasping and aligning of the ribbon cable, and mating a pair of cable connectors, was successfully implemented.