This　work　investigates　the　frequency　diverse　array　(FDA)-assisted　covert　communication　system,　in　which　the　general　beampattern　generated　by　FDA　is　utilized　to　establish　a　secure　region　for　the　legitimate　user,　thereby　improving　the　system＇s　covert　performance.　Specifically,　we　first　derive　a　closedform　expression　of　the　system　covertness　constraint　based　on　Kullback-Leibler　(KL)　divergence.　Then,　when　the　FDA　beampattern　power　attenuates　to　a　value　that　satisfies　the　covertness　constraint,　the　secure　region　is　defined　and　the　corresponding　boundary　expression　of　which　is　also　deduced.　Furthermore,　to　reduce　the　risk　of　covert　transmission　being　detected,　the　secure　region　minimization　problem　is　established,　while　the　methods　based　on　the　Rayleigh-Ritz　theorem　and　nonlinear　programming　are　formulated　to　solve　the　optimization　problem,　respectively.　Simulation　results　compare　the　different　frequency　schemes　and　show　that　the　optimized　frequency　leads　to　a　smaller　area　of　the　secure　region　and　lower　KL　divergence　than　the　benchmark　schemes.　©　2024　IEEE.