Traditional　recommender　systems　only　utilize　a　single　user-item　interaction　behavior　as　the　optimization　target　behavior.　However,　multi-behavior　recommender　systems　leverage　multiple　user　behaviors　as　auxiliary　behaviors(favorite　and　page　view),　which　is　more　practical.　Therefore,　recommender　systems　by　exploring　patterns　of　multiple　behaviors　are　of　great　significance　in　improving　performance.　Many　previous　works　toward　multi-behavior　recommendation　fail　to　capture　user　preference　intensity　for　different　items　in　the　heterogeneous　graph.　Meanwhile,　they　also　ignore　high-order　relationships　that　incorporate　user　different　preference　intensity　into　user-item　heterogeneous　interactions.　To　solve　the　above　challenges,　we　propose　a　novel　multi-behavior　recommendation　model　named　neighbor-aware　attention-based　heterogeneous　relation　network　model　in　E-commerce　recommendation　(NAH).　NAH　leverages　the　attention　propagation　layer　to　capture　user　preference　intensity　for　different　items　and　employs　a　composition　method　to　incorporate　relation　embeddings　into　node　embeddings　for　high-order　propagation.　Experiment　results　on　two　real-world　datasets　verify　the　effectiveness　of　our　model　in　the　multi-behavior　task　by　comparing　it　with　some　start-of-the-art　methods.　Further　studies　verify　that　our　model　has　a　significant　effect　on　exploring　high-order　information　and　cold-start　users　who　have　few　user-item　interaction　records.　©　2023,　The　Author(s),　under　exclusive　licence　to　Springer　Science+Business　Media,　LLC,　part　of　Springer　Nature.