The robotic hand plays an extremely significant role in completing various robotic tasks, especially for a robot to complete different grasping tasks. In this paper, we propose a novel multi-fingered bionic hand with variable stiffness for robotic grasp. First, based on the analysis of the human hand, we design the modular finger with variable stiffness mechanism and the flexible thumb with dual-link independent mechanism. Second, the multi-fingered bionic hand composed of three modular fingers and one flexible thumb is presented, which possesses 14 degrees-of-freedom (DoFs). Then, the parameters of the designed hand are analyzed to obtain the stiffness characteristics and working space. Furthermore, the grasping control method based on position control and force control is proposed for robotic grasp. Finally, a series of experiments are designed to verify the effectiveness of the designed hand and the proposed method. The experimental results show that (1) the designed variable stiffness mechanism can be used to adjust the stiffness of hand fingers, (2) the proposed method can effectively control the grasping force under different stiffness conditions, and (3) the designed hand can successfully grasp different types of objects by various grasping strategies.