This paper presents a study on bioinspired rigid-flexible coupling adaptive compliant motion control of a robot gecko with hybrid actuation for space stations. The biomimetic robot gecko is made of a rigid trunk, four motor-driven active legs with dual-degree-of-freedom shoulder joints, and four pneumatic flexible pleated active attachment–detachment feet. The adaptive impedance model consists of four input parameters: the inertia coefficient, stiffness coefficient, damping coefficient, and segmented expected plantar force. The robot gecko is equipped with four force sensors mounted on its four feet, from which the normal force of each foot can be sensed in real-time. Based on the sensor signal, the variable stiffness characteristics of the feet in different states are analyzed. Furthermore, an adaptive active compliance control strategy with whole-body rigidity–flexibility-force feedback coupling is proposed for the robot gecko. Four sets of experiments are presented, including open-loop motion control, static anti-interference experiment, segmented variable stiffness experiment, and adaptative compliant motion control, both in a microgravity environment. The experiment results indicated that the presented control strategy worked well and the robot gecko demonstrates the capability of stable attachment and compliant detachment, thereby normal impact and microgravity instability are avoided. It achieves position tracking and force tracking while exhibiting strong robustness for external disturbances.