The on-orbit refueling operation can be regarded as a dual-axis hole assembly problem. The refueling tool needs to be inserted into the target smoothly, minimizing contact force during the process to reduce interference with the satellite. This paper proposes a novel admittance control method for on-orbit refueling operations using a symmetric stiffness matrix. The damping matrix selection and control system stability are demonstrated using the root locus method. In contrast to traditional diagonal stiffness matrix designs, the symmetric stiffness matrix introduces coupling between different dimensions. This allows for the reduction of the robot’s contact force and enhances its adaptability to varying environmental conditions. The experimental results of the double peg-in-hole assembly confirm the effectiveness of this method. Compared to the traditional diagonal stiffness matrix design, the method proposed in this article can significantly decrease the contact force during the insertion process, thus enabling a smoother completion of the task.