This paper proposes a novel sensor-less force control method by an underactuated wire-driven robotic finger. This robotic hand contains Twisted round-belt actuator that yields contraction forces produced by twisting an elastic round-belt. This mechanism provides high-resolution control of both the force and joint angle in manipulation tasks. First, we explain the basic mechanism of the articulated two-fingered robotic hand having Twisted round-belt actuator, and mention its features by some experiments. Second, we show experimental results of round-belt contraction force on the basis of two parameters such as number of twist and tension of the belt, resulting in fingertip force estimation which is applicable to sensor-less force control. Finally, we apply this estimation method to the robotic hand, and experimentally demonstrate secure force control in sensor-less configuration at the fingertip.