Myoelectric prosthetic hands are intended to replace the function of the amputee's lost arm. Therefore, developing robotic prosthetics that can mimic not only the appearance and functionality of humans but also characteristics unique to human movements is paramount. Although the impedance model was proposed to realize biomimetic control, this model cannot replicate the characteristics of human movements effectively because the joint angle always converges to the equilibrium position during muscle relaxation. This paper proposes a novel biomimetic control method for myoelectric prosthetic hands integrating the impedance model with the concept of the $λ$-type muscle model. The proposed method can dynamically control the joint equilibrium position, according to the state of the muscle, and can maintain the joint angle naturally during muscle relaxation. The effectiveness of the proposed method is evaluated through simulations and a series of experiments on non-amputee participants. The experimental results, based on comparison with the actual human joint angles, suggest that the proposed method has a better correlation with the actual human motion than the conventional methods. Additionally, the control experiments showed that the proposed method could achieve a natural prosthetic hand movement similar to that of a human, thereby allowing voluntary hand opening and closing movements.