Abstract: A method of controlled flying around of space-based surveillance was proposed to observe continuously the specific surface of GEO slow-spinning space target. Firstly, a relative motion model of target and space-based platform was established. And then, analyzing the expected relative orbit model of arbitrary spin axis, a single cycle controlled flying around model and a multi-cycle spiral approaching controlled flying around model were designed. Time constrained multi-pulse control was used to realize controlled flying around. Finally, the controlled flying around orbit with different flying radius, different number of pulses and different flying periods was simulated and analyzed to provide and verify a multi-cycle spiral approaching controlled flight strategy. The results show that, by mapping the attitude changes of GEO slow-spinning space target to the design of relative controlled flying around orbit, the continuous surveillance of the specific surface can be realized. The simulation results and conclusions can provide a significant reference for engineering application.