For slowly rotating non-cooperative target, two fast fly-around collision avoidance controllers are designed based on the theory of sliding mode control and artificial potential function, which can realize safe fast fly-around. By considering the non-cooperative satellite geometry, the ellipsoid collision-avoidance-zone model is established, and fast fly-around collision avoidance is realized for the spherical collision-avoidance-zone. Based on the fully nonlinear relative motion equation, the fast fly-around collision avoidance controllers are designed respectively for systems with and without knowledge of external disturbances’ upper bound, both of which can strictly guarantee the safety of fast fly-around. The asymptotic stability is proved by Lyapunov theory. The numerical simulation is performed to verify the effectiveness of the proposed controllers.