A　V-cycle　multigrid　method　for　the　Hellan-Herrmann-Johnson　(HHJ)　discretization　of　the　Kirchhoff　plate　bending　problems　is　developed　in　this　paper.　It　is　shown　that　the　contraction　number　of　the　V-cycle　multigrid　HHJ　mixed　method　is　bounded　away　from　one　uniformly　with　respect　to　the　mesh　size.　The　uniform　convergence　is　achieved　for　the　V-cycle　multigrid　method　with　only　one　smoothing　step　and　without　full　elliptic　regularity　assumption.　The　key　is　a　stable　decomposition　of　the　kernel　space　which　is　derived　from　an　exact　sequence　of　the　HHJ　mixed　method,　and　the　strengthened　Cauchy　Schwarz　inequality.　Some　numerical　experiments　are　provided　to　confirm　the　proposed　V-cycle　multigrid　method.　The　exact　sequences　of　the　HHJ　mixed　method　and　the　corresponding　commutative　diagram　is　of　some　interest　independent　of　the　current　context.