This　paper　focuses　on　the　existence　and　global　exponential　stability　of　periodic　solutions　for　feedback　control　complex　dynamical　networks　with　time-varying　delays　(FCCDND).　Combining　the　continuation　theorem　of　coincidence　degree　theory,　a　combinatorial　identity　about　Kirchhoff＇s　matrix　tree　theorem　in　graph　theory,　and　Lyapunov　method,　a　novel　method　is　established　to　investigate　the　existence　and　global　exponential　stability　of　periodic　solutions　for　FCCDND.　Finally,　the　effectiveness　and　practicability　of　our　results　are　illustrated　by　a　numerical　example　and　its　simulation.　(c)　2021　Elsevier　Ltd.　All　rights　reserved.