Recently,　assembly　line　balancing　problem　with　uncertain　task　time　gains　more　and　more　attention　in　the　literature.　Task　time　uncertainty　may　overload　workstations.　Uncertain　task　time　attributes　were　studied　in　the　frameworks　of　the　probability　theory.　In　this　paper,　we　use　a　new　method,　which　is　the　uncertainty　theory,　to　model　the　uncertain　task　time　as　the　historical　task　time　information　is　unavailable.　We　incorporate　the　uncertainty　into　the　constraints　of　the　type-1　U-shaped　assembly　line　balancing　problem.　We　derive　some　useful　theorems　related　to　the　optimal　solutions.　Further,　we　develop　an　algorithm　based　on　the　branch　and　bound　remember　algorithm　to　solve　the　proposed　problem.　Finally,　numerical　studies　are　conducted　to　illustrate　our　model.　(C)　2019,　IFAC　(International　Federation　of　Automatic　Control)　Hosting　by　Elsevier　Ltd.　All　rights　reserved.