Unmanned aerial vehicle (UAV) communications and networks are promising technologies in the forthcoming fifth-generation wireless communications. However, they have the challenges for realizing secure communications. In this paper, we consider to construct a virtual antenna array consists UAV elements and use collaborative beamforming (CB) to achieve the UAV secure communications with different base stations (BSs), subject to the known and unknown eavesdroppers on the ground. To achieve a better secure performance, the UAV elements can fly to optimal positions with optimal excitation current weights for performing CB transmissions. However, this leads to extra motion energy consumptions. We formulate a secure communication multi-objective optimization problem (MOP) of UAV networks to simultaneously improve the total secrecy rates, total maximum sidelobe levels (SLLs) and total motion energy consumptions of UAVs by jointly optimizing the positions and excitation current weights of UAVs, and the order of communicating with different BSs. Due to the complexity and NP-hardness of the formulated MOP, we propose an improved multi-objective dragonfly algorithm with chaotic solution initialization and hybrid solution update operators (IMODACH) to solve the problem. Simulation results verify that the proposed IMODACH can effectively solve the formulated MOP and it has better performance than some other benchmark approaches.