Unmanned aerial vehicle (UAV) assisted wireless communication is essential for the next-generation mobile networks. In coping with the increased dynamics in UAV networks, the design of control information transmission is essential, requiring ultra reliability, low latency, and high security. In this paper, considering both the large-scale path loss and the Nakagami-m small-scale fading, we investigate the secrecy performance of UAV control information transmission in a NOMA ground-air network with an external flying eavesdropper. A spherical secrecy protection zone is set, and the closed-form expressions for average secure BLER and average achievable secrecy throughput are derived. After that, the asymptotic performance in the high SNR regime is analyzed to get more insights. Ultimately, simulation results verify the accuracy of analysis.