To solve the complex structure, poor flexibility, and heavyweight of the rigid robotic hand, a pneumatic four-finger flexible robotic hand is developed in this paper. The robotic hand is about 1.3 times as large as that of a human hand and each finger is composed of a single multi-drive bending joint. The kinematic model of the robotic hand is established by using homogeneous coordinate transformation matrix. Through the simulation experiment of the robotic hand structure, the trajectory, and workspace of the robotic hand are established. According to the experimental results of grasping performance of the robotic hand, the grasping forces of different geometric positions along the finger axis are obtained. The results show that the robotic hand can realize a variety of grasping modes, has flexible action and strong adaptive ability; it can grasp, hold, and pinch, as well as stably grasp objects such as cylinder, box, and sphere. In pinch grasp mode, the robotic hand can grip objects as thin as 1 mm and the diameter of the grasped object varies from 28 mm to 160 mm; the maximum mass that the robotic hand can grasp an object with a diameter of 90 mm under 0.35 MPa is 1386 g.