This paper investigates the time-varying formation control problem for multiple unmanned aerial vehicle (multi-UAV) systems with unknown uncertainties and varying time delays. Firstly, a radial basis function neural network (RBFNN) is adopted to estimate the lumped model uncertainties online for compensation. Then, a novel RBFNN-based fully distributed adaptive control scheme consisting of control law to stabilize the system and adaptive law to adjust RBFNN weights is developed to tackle the time-varying formation tracking problem in the presence of varying time delay. The uniformly ultimately boundedness (UUB) of the formation tracking errors is theoretically analyzed through Lyapunov approach. Comparative simulation results demonstrate the effectiveness of the control and adaptive laws proposed in this paper.