In　this　paper,　we　study　the　problem　of　maximizing　a　sequence　submodular　function　in　the　streaming　setting,　where　the　utility　function　is　defined　on　sequences　instead　of　sets　of　elements.　We　encode　the　sequence　submodular　maximization　with　a　weighted　digraph,　in　which　the　weight　of　a　vertex　reveals　the　utility　value　in　selecting　a　single　element　and　the　weight　of　an　edge　reveals　the　additional　profit　with　respect　to　a　certain　selection　sequence.　The　edges　are　visited　in　a　streaming　fashion　and　the　aim　is　to　sieve　a　sequence　of　at　most　k　elements　from　the　stream,　such　that　the　utility　is　maximized.　In　this　work,　we　present　an　edge-based　threshold　procedure,　which　makes　one　pass　over　the　stream,　attains　an　approximation　ratio　of　(1　/　(2　Δ+　1)　-　O())　,　consumes　O(kΔ/　)　memory　source　in　total　and　O(log　(kΔ)　/　)　update　time　per　edge,　where　Δ　is　the　minimum　of　the　maximal　outdegree　and　indegree　of　the　directed　graph.　©　2020,　Springer　Science+Business　Media,　LLC,　part　of　Springer　Nature.