This paper investigates a formation control problem of fixed-wing Unmanned Aerial Vehi-cle (UAV) swarms. A group-based hierarchical architecture is established among the UAVs, which decomposes all the UAVs into several distinct and non-overlapping groups. In each group, the UAVs form hierarchies with one UAV selected as the group leader. All group leaders execute coordinated path following to cooperatively handle the mission process among different groups, and the remaining followers track their direct leaders to achieve the inner-group coordination. More specifically, for a group leader, a virtual target moving along its desired path is assigned for the UAV, and an updating law is proposed to coordinate all the group leaders' virtual targets;for a follower UAV, the distributed leader-following formation control law is proposed to make the follower's heading angle coincide with its direct leader, while keeping the desired relative position with respect to its direct leader. The pro-posed control law guarantees the globally asymptotic stability of the whole closed-loop swarm system under the control input constraints of fixed-wing UAVs. Theoretical proofs and numerical simula-tions are provided, which corroborate the effectiveness of the proposed method.