Impedance control is an important technology used in the grasping control of a robot hand. Numerous studies related to grasping algorithms have been reported in recent years, with the contact force between robot fingers and the object to be grasped being primarily discussed in most cases. Generally, a coupling effect occurs between the internal loop of the grasping operation and the external loop of the interaction with the environment when a multi-fingered robot hand is used to complete a contact task. Therefore, a robot hand cannot hold an object using a large external force to complete a wide range of tasks by applying the conventional method. In this paper, the coupling of the internal/external forces occurring in grasping operations using multiple fingers is analysed. Then, improved impedance control based on the previous method is proposed as an effective tool to solve the problem of grasping failure caused by single-finger contact. Furthermore, a method for applying the improved grasping algorithm to the admittance control of a robot hand-arm system is also proposed. The proposed method divides the impedance effect into the grasping control of the hand and the cooperative control of the arm, so that expanding the task space and increasing the flexibility of impedance adjustment can be achieved. Experiments were conducted to demonstrate the effectiveness of the proposed method.