As the demand of on-orbit service tasks in unstructured environments surges, traditional rigid robotic arms face significant challenges due to bulkiness, insufficient degrees of freedom and poor flexibility. To this end, this paper proposes an innovative design of a space continuum robot (SCR) based on spring and bionic muscle antagonistic actuation, aiming to enhance the robot’s adaptability in constrained spaces and non-cooperative target surfaces. The design employs a spring-supported rod with a symmetrical layout of bionic muscle synergistic mechanism, and determines the number of spacer disks through a multi-objective optimization method to achieve an increase in axial percentage of extension/contraction to 63% and structural lightness (the mass is reduced to 47% of that of the traditional solution). The robot kinematic and dynamic model is established based on Cosserat rod theory, and the workspace and bending performance are verified through simulation. The results of two typical mission experiments show that the robot end trajectory is basically consistent with the model prediction. This study provides an efficient and reliable solution for spacecraft on-orbit inspection and maintenance, and significantly advances the application potential of continuum robots in space operations.