A　modified　weak　Galerkin　(MWG)　finite　element　method　is　developed　for　solving　the　biharmonic　equation.　This　method　uses　the　same　finite　element　space　as　that　of　the　discontinuous　Galerkin　method,　the　space　of　discontinuous　polynomials　on　polytopal　meshes.　But　its　formulation　is　simple,　symmetric,　positive　definite,　and　parameter　independent,　without　any　of　six　inter-element　face-integral　terms　in　the　formulation　of　the　discontinuous　Galerkin　method.　Optimal　order　error　estimates　in　a　discrete　H2　norm　are　established　for　the　corresponding　finite　element　solutions.　Error　estimates　in　the　L2　norm　are　also　derived　with　a　sub-optimal　order　of　convergence　for　the　lowest-order　element　and　an　optimal　order　of　convergence　for　all　high-order　of　elements.　The　numerical　results　are　presented　to　confirm　the　theory　of　convergence.　©　2020,　Shanghai　University.