With the development of human space exploration, the space environment is gradually filled with abandoned satellite debris and unknown micrometeorites, which will seriously affect capture motion of space robot. Hence, a novel fast collision-avoidance trajectory planning strategy for a dual-arm free-floating space robot (FFSR) with predefined-time pose feedback will be mainly studied to achieve micron-level tracking accuracy of end-effector in this paper. However, similar to control, the exponential feedback results in larger initial joint angular velocity relative to proportional feedback. Firstly, a pose-error-based kinematic model of the FFSR will be derived from a control perspective. Then, a cumulative dangerous field (CDF) collision-avoidance algorithm is applied in predefined-time trajectory planning to achieve micron-level collision-avoidance trajectory tracking precision. In the end, a GA-based optimization algorithm is used to optimize the predefined-time parameter to obtain a motion trajectory of low joint angular velocity of robotic arms. The simulation results verify our conjecture and conclusion.