Quantum　computing　has　the　characteristics　of　superposition　and　entanglement,　which　make　quantum　computers　have　natural　parallelism　and　be　faster　and　more　efficient　than　classical　computers.　The　quantum　matrix　multiplier　proposed　in　this　paper　improves　the　efficiency　of　matrix　multiplication　algorithms,　and　also　meets　the　needs　of　many　quantum　algorithms　that　use　matrix　multiplication　as　an　intermediate　step.　In　our　scheme,　the　data　of　two　matrices　are　superimposed　and　stored　in　the　basis　state　of　quantum　states　respectively.　Quantum　multipliers　and　quantum　comparators　are　used　to　make　up　the　quantum　output　matrix.　When　a　M　x　N　matrix　and　a　N　x　S　matrix　are　multiplied,　the　time　complexity　is　reduced　from　classical　O(MNS)　to　quantum　O(MS　log(2)N),　and　the　space　complexity　is　reduced　from　classical　O(MN　+　NS　+　MS)　to　quantum　O(1).　Moreover,　unlike　the　existing　quantum　matrix　multiplication　algorithms,　our　calculation　results　are　directly　stored　in　the　basis　state,　without　having　to　rely　on　measurement　to　get　the　result,　and　can　be　used　as　an　intermediate　module　of　complex　quantum　algorithms.