The　properties　of　two-machine　no-wait　flow-shop　scheduling　problem,　with　a　non-resumable　unavailable　interval　are　studied.　This　research　discusses　two　cases:　a　non-resumable　unavailable　interval　in　the　first　and　second　machines　respectively.　The　problems’　complexities　are　proved　to　be　NP-hard.　The　Gilmore　and　Gomory　Algorithm　(GGA)　is　applied　to　minimize　the　makespan,　and　the　conditions　that　GGA　yields　the　optimal　solutions　are　presented.　Sixty　numerical　examples　with　ten-job　and　two-machine　are　generated　to　test　the　proposed　theorems.　Compared　to　the　results　obtained　by　the　Johnson　algorithm,　the　GGA　algorithm　yields　an　8.15%　improvement　on　average.　Moreover,　the　worst-case　performance　ratios　of　GGA　are　proved　to　be　2.　©　2017　Chinese　Institute　of　Industrial　Engineers.