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The space tethered-net is an important tool for space debris capture. But its rebound movement limits its effective working distance. To solve this issue, a passive control method using “Energy dissipation band (EDB)” is proposed in this paper. A semi-spring damper model of the EDB is first built and verified by the tests, and then the strengths of the bands are optimized with Radial Basis Function assisted optimization method with Batch infill Sampling criterion (RBFBS). Simulation results show that this passive control method can significantly increase the effective work distance of the space tethered-net, and RBFBS algorithm is able to optimize the strengths of the EDBs effectively and efficiently. This paper provides a new idea for the optimal design of the space tethered-net, which can be applied to the future flexible capture tasks.