In　a　gesture　recognition　system　based　on　surface　electromyogram　(sEMG)　signals,　the　recognition　model　established　by　existing　users　cannot　directly　generalize　to　the　across-user　scenarios　due　to　the　individual　variability　of　sEMG　signals.　In　this　article,　we　propose　an　adaptive　learning　method　to　handle　the　problem.　The　muscle　synergy　is　chosen　as　the　feature　vector　because　it　can　well-characterize　the　neural　origin　of　movement.　The　initial　train　set　is　composed　of　representative　samples　extracted　from　the　synergy　matrix　of　the　existing　user.　When　the　new　users　use　the　system,　the　label　is　obtained　by　the　adaptive　K　nearest　neighbor　algorithm　(KNN).　The　recognition　process　does　not　require　the　pre-experiment　for　new　users　due　to　the　introduction　of　adaptive　learning　strategy,　namely,　the　qualified　data　and　the　label　of　new　user　data　evaluated　by　a　risk　evaluator　are　used　to　update　the　train　set　and　KNN　weights,　so　as　to　adapt　to　the　new　users.　We　have　tested　the　algorithm　in　DB1　and　DB5　of　Ninapro　databases.　The　average　recognition　accuracy　is　68.04,　73.35,　and　83.05%　for　different　types　of　gestures,　respectively,　achieving　the　effects　of　the　user-dependent　method.　Our　study　can　avoid　the　re-training　steps　and　the　recognition　performance　will　improve　with　the　increased　frequency　of　uses,　which　will　further　facilitate　the　widespread　implementation　of　sEMG　control　systems　using　pattern　recognition　techniques.