Quantum satellite communication is a research hotspot in the field of quantum communication, which has the characteristics of wide coverage, high communication efficiency and strong security. The construction strategy of the quantum communication network is an essential part of quantum communication. However, the construction strategy of quantum air communication network has not been studied yet so far. In this paper, according to the characteristics of flying goose array and principle of bionics, a simulated wild goose group Λ quantum air communication network topology is proposed, which can be divided into single-head node Λ type and multi-head node Λ type. Based on Greenberger-Horne-Zeilinger (GHZ) state particles, a certifiable QSDC inter-network communication system and a GHZ-EPR quantum teleportation communication system are established. The bit error rate, energy consumption, throughput, and other parameters are studied. After theoretical analysis and experimental measurement, for the single-head node Λ network structure in the environment where the average power spectral density of noise is 2 dB/m, when the communication distance between the head node and the child node is less than 400 m, the bit error rate is less than 0.094; if the communication distance increases from 400 m to 1000 m, the bit error rate increases rapidly, reaching 0.585; when the number of child nodes on one side increases from 2 to 7, the throughput decreases from 110.6 kb/s to 46.45 kb/s. For example, when the total number of nodes is 21, the single-head node Λ network structure saves 32.6% energy but reduces the throughput to 23.9 kb/s. By comparison, the multi-head node Λ network structure with 21 nodes saves 29.3% energy and achieves throughput of 163.4 kb/s. The above studies show that the quantum air network with the structure of imitation goose group array has good network scalability, excellent information security and flexible network structure.