Human muscles can generate force and stiffness during contraction. When in contact with objects, human hands can achieve compliant grasping by adjusting the grasping force and the muscle stiffness based on the object’s characteristics. To realize humanoid-compliant grasping, most prosthetic hands obtain the stiffness parameter of the compliant controller according to the environmental stiffness, which may be inconsistent with the amputee’s intention. To address this issue, this paper proposes a compliant grasp control method for an underactuated prosthetic hand that can directly obtain the control signals for compliant grasping from surface electromyography (sEMG) signals. First, an estimation method of the grasping force is established based on the Huxley muscle model. Then, muscle stiffness is estimated based on the muscle contraction principle. Subsequently, a relationship between the muscle stiffness of the human hand and the stiffness parameters of the prosthetic hand controller is established based on fuzzy logic to realize compliant grasp control for the underactuated prosthetic hand. Experimental results indicate that the prosthetic hand can adjust the desired force and stiffness parameters of the impedance controller based on sEMG, achieving a quick and stable grasp as well as a slow and gentle grasp on different objects.