In this paper, we propose a forceps grasper using a soft actuator that can estimate grasping force. The grasper consists of a small cylinder and a slider-crank mechanism embedded at the tip of the forceps. A pneumatic soft actuator made of silicone is fabricated and inserted in the cylinder. The grasper is actuated by inflating the soft actuator. It causes no leakage of air, as well it is lightweight and disposable. The developed soft actuator has a built-in strain gauge to measure the displacement of the actuator. By combing the measurements of the strain gauge and the internal pressure, it can estimate the grasping force. We investigated the relationship between the air pressure in the soft actuator and the opening angle of the grasper in order to estimate the force without a force sensor. First, the soft actuator is pressurized from 0kPa to 160kPa at intervals of 10kPa, and the opening angle of the grasper is measured for each pressure without any load on the grasper. The linearity of the soft actuator between the pressure and the opening angle is confirmed. Then, the experiment with the same protocol is conducted while the grasper grasps a force sensor. The estimated force and the output of the force sensor are compared to show the effectiveness of the proposed method.