Considering the distributed communication network, the fully distributed formation building and keeping control problems for multiple unmanned aerial vehicles(UAVs) are studied. Adaptive coupling gains are designed based on sliding mode and adaptive methods, and then a novel finite-time formation controller is designed according to the relative state between neighbor UAVs and coupling gains. The proposed algorithm removes the limitation of global information, such as the range and topology of the communication network and the state of the Leader UAV. Based on the Lyapunov theory, the formation errors can converge to a small boundary adjustable neighborhood. Simulation of the three dimensional motion for multiple UAVs formation is conducted. The results show that the proposed algorithm can achieve the finite time fully distributed formation forming and keeping of UAVs.