With　the　no-idle　constraint,　a　machine　has　to　process　a　job　after　finishing　the　previous　one　without　any　interruption.　The　start　time　of　the　first　job　on　each　machine　must　thus　be　delayed　to　meet　this　condition.　In　this　paper,　a　new　Iterated　Greedy　Algorithm　(IGA)　is　presented　for　no-idle　flowshop　scheduling　with　the　objective　of　minimizing　the　total　tardiness.　For　the　initialization　phase,　a　variant　of　the　NEH　procedure　is　developed.　Then,　we　propose　a　new　variable　local　search　based　on　an　insert　move　with　two　different　job　selection　mechanisms.　A　tardiness-guided　job　selection　procedure,　a　job-dependent　parameter　and　an　insert-swap　based　method　are　further　introduced　in　the　destruction-construction　phases.　While　most　of　the　related　studies　have　used　a　fixed　probability　for　accepting　new　or　non-improving　solutions,　we　propose　a　time-dependent　probability　that　allows　our　algorithm　to　focus　on　exploration　in　early　iterations　and　exploitation　in　later　iterations.　Comprehensive　computational　experiments　show　that　the　proposed　IGA　is　superior　in　terms　of　solution　quality　than　state-of-the-art　algorithms　for　the　problem　at　hand.　As　a　result,　more　than　50%　of　the　existing　best　solutions　for　the　benchmark　instances　tested　have　been　updated.　(C)　2019　Elsevier　Ltd.　All　rights　reserved.