The linkschedulingis to determine which links should be scheduled at what times, each of which is a (sender, receiver) communication pair used to realize wireless transmission of a message. It is an appealing solution to fulfill the resource-constrained and latency requirements of unmanned aerial vehicle (UAV) swarms. However, most existing link scheduling algorithms primarily focus on the throughput or latency in wireless communication, neglecting the protection against the eavesdropping attack due to the openness of UAV swarms, thereby leading to unsafe message dissemination. To address this issue, we consider integrating the covert communication into the link scheduling by concealing the very existence of message transmission. We first present a successive interference cancellation-based link diversity partition (SIC-LDP) algorithm in the context of the physical interference model, to maximize the number of concurrently transmitting links in a single time round, also called the maximum link scheduling (MLS) issue. Then, using a friendly jammer, we further propose a covertness-aware SIC-LDP algorithm (named SIC-CLDP) to resolve the MLS, as well as to defend against the eavesdropping attack. Both SIC-LDP and SIC-CLDP algorithms are proven to have constant approximation ratios. Next, implementing SIC-LDP and SIC-CLDP repeatedly can minimize the number of time rounds schedulingnparticipating links, termed the shortest link scheduling (SLS) issue, with an approximation ratio ofO(lnn). Lastly, theoretical proofs and simulation results demonstrate the correctness, covertness, and efficiency of our proposed algorithms under the eavesdropping attack.