For　the　biharmonic　equation　or　this　singularly-perturbed　biharmonic　equation,　lower　order　nonconforming　finite　elements　are　usually　used.　It　is　difficult　to　construct　high　order　C1　conforming,　or　nonconforming　elements,　especially　in　3D.　A　family　of　any　quadratic　or　higher　order　weak　Galerkin　finite　elements　is　constructed　on　2D　polygonal　grids　and　3D　polyhedral　grids　for　solving　the　singularly-perturbed　biharmonic　equation.　The　optimal　order　of　convergence,　up　to　any　order　the　smooth　solution　can　have,　is　proved　for　this　method,　in　a　discrete　H-2　norm.　Under　a　full　elliptic　regularity　H-4　assumption,　the　L-2　convergence　achieves　the　optimal　order　as　well,　in　2D　and　3D.　Numerical　tests　are　presented　verifying　the　theory.