In order to eliminate the limitation of the Space Tether-Net System in the field of maneuver and control, we propose the Maneuvering-Net Space Robot System (MNSRS) in this paper, which can capture and remove the space debris dexterously. We focus on the approaching phase towards the space debris, which is a challenging problem for the MNSRS, especially the coupled dynamics modelling and configuration control problems. Firstly the system and mission overview of the MNSRS is described in detail. After that, a coupled dynamics modelling, which divides the MNSRS into finite mass points connected with massless springs, is established to describe dynamic characteristics of the MNSRS in approaching phase. Then the configuration variation of the MNSRS in approaching phase is analyzed. Finally the configuration control of the MNSRS in approaching phase is investigated.