Recommendation　system　is　a　kind　of　information　filtering　system,　which　plays　an　increasingly　important　role　in　the　era　of　big　data.　In　this　work,　we　present　a　novel　quantum　recommender　system,　which　can　also　be　regarded　as　a　quantum　version　of　the　matrix　reconstruction　algorithm.　In　order　to　obtain　two　factors　in　the　quantum　state　form,　a　quantum　version　of　the　alternating　least　squares　algorithm　is　designed.　And　based　on　the　factor　matrices,　the　reconstruction　matrix　of　the　original　rating　matrix　is　calculated.　The　complexity　analysis　shows　that　our　quantum　algorithm　may　achieve　an　exponential　speedup　relative　to　the　classical　counterpart　under　certain　conditions.