This paper addresses the target enclosing control problem for fixed-wing UAVs in three dimensional space with a novel attractive vector approach. Firstly, by analyzing the properties of the desired ring motion plane in 3D space with an arbitrary desired direction vector, an attractive vector approach that provides a control direction for solving the target enclosing problem is established. Then, based on the attractive vector, the desired course angle and flight path angle are constructed, respectively. Thereafter, the target enclosing control law that guarantees the desired ring motion plane is perpendicular to the arbitrary desired direction vector in 3D space is designed, and the corresponding stability is analyzed by the Lyapunov function approach. Finally, the effectiveness of the proposed approach is validated by both numerical simulations and experiments.