The Unmanned Aerial Vehicles (UAVs) become more and more popular due to various potential application fields. This paper studies the distributed leader-follower formation flight control problem of multiple UAVs with uncertain parameters for both the leader and followers. This problem has not been addressed in the literature. Most of the existing literature considers the leader-follower formation control strategy with parametric uncertainty for the followers. However, they do not take the leader parametric uncertainty into account. Meanwhile, the distributed control strategy depends on less information interactions and is more likely to avoid information conflict. The dynamic model of the UAVs is established based on the aerodynamic parameters. The establishment of the topology structure between a collection of UAVs is based on the algebraic graph theory. To handle the parametric uncertainty of the UAVs dynamics, a multivariable model reference adaptive control (MRAC) method is addressed to design the control law, which enables follower UAVs to track the leader UAV. The stability of the formation flight control system is proved by the Lyapunov theory. Simulation results show that the proposed distributed adaptive leader-following formation flight control system has stronger robustness and adaptivity than the fixed control system, as well as the existing adaptive control system.