This paper investigates the time-varying formation control problem for multiple unmanned aerial vehicle (multi-UAV) systems with time-varying delays and jointly connected topologies. Firstly, a consensus based formation control law is proposed to realize and maintain the desired time-varying formation in presence of time-varying delays and jointly connected topologies. Then, a sufficient condition in terms of linear matrix inequalities (LMI) is derived for formation control and the stability of the close-loop system is analyzed by employing Lyapunov-Krasovskii function. Finally, two task-oriented formation transformation cases are simulated to verify the effectiveness of the proposed control law, where the first is to shape varying regular hexagon, and the second is to avoid multiple obstacles.