This paper describes the development of a 6-axis robot's finger force/moment sensor, which measures forces Fx, Fy, Fz, and moments Mx, My, Mz simultaneously, for stably grasping an unknown object. In order to safely grasp an unknown object using the robot's gripper, it should measure the force in the gripping direction and the force in the gravity direction, and perform the force control using the measured forces. Thus, the robot's gripper should be composed of 6-axis robot's finger force/moment sensor that can measure forces Fx, Fy, Fz, and moments Mx, My, Mz simultaneously. In this paper, the 6-axis robot's finger force/moment sensor for measuring forces Fx, Fy, Fz, and moments Mx, My, Mz simultaneously was newly modeled using several parallel-plate beams, designed, and fabricated. The characteristic test of made sensor was performed. and the result shows that interference errors of the developed sensor are less than 3%. Also, Robot's gripper with the 6-axis robot's finger force/moment sensor for the characteristic test of force control was manufactured, and the characteristic test for grasping an unknown object was performed using it. The fabricated gripper could grasp an unknown object stably. Thus, the developed 6-axis robot's finger force/moment sensor may be used for robot's gripper.