This　paper　proposes　a　secure　downlink　multi-user　transmission　scheme　enabled　by　a　flexible　unmanned　aerial　vehicle　base　station　(UAV-BS)　and　non-orthogonal　multiple　access　(NOMA).　According　to　their　heterogeneous　service　requirements,　multiple　legitimate　users　are　categorized　as　security-required　users　(SUs)　and　quality　of　service　(QoS)-required　users　(QUs),　while　these　QUs　can　potentially　act　as　internal　eavesdroppers　which　are　curious　about　the　secrecy　transmissions　of　SUs.　In　such　a　context,　our　goal　is　to　maximize　the　achievable　minimum　secrecy　rate　among　SUs　through　the　joint　optimization　of　user　scheduling,　power　allocation,　and　trajectory　design,　subject　to　the　QoS　requirements　of　QUs　and　the　mobility　constraint　of　UAV-BS.　Due　to　the　non-convexity　of　the　problem,　an　efficient　iterative　algorithm　is　firstly　proposed,　based　on　the　alternative　optimization　(AO)　and　successive　convex　approximation　(SCA)　methods　and　along　with　a　penalty-based　algorithm　to　deal　with　the　introduced　binary　integer　variables,　to　obtain　a　sub-optimal　solution.　Then,　we　propose　an　SUs-oriented　low-complexity　algorithm　by　taking　advantage　of　the　inherent　characteristics　of　the　optimization　problem,　which　can　efficiently　reduce　the　computational　complexity　and　can　act　as　a　reasonable　initial　solution　for　the　previous　iterative　algorithm　to　achieve　better　performance.　Finally,　the　superiority　of　our　proposed　scheme　compared　with　the　conventional　orthogonal　multiple　access　(OMA)　one　is　validated　by　numerical　simulation　results.