This　paper　is　devoted　to　a　discontinuous　Galerkin　(DG)　method　for　nonlinear　quasistatic　poroelasticity　problems.　The　fully　implicit　nonlinear　numerical　scheme　is　constructed　by　utilizing　DG　method　for　the　spatial　approximation　and　the　backward　Euler　method　for　the　temporal　discretization.　The　existence　and　uniqueness　of　the　numerical　solution　is　proved.　Then　we　derive　the　optimal　convergence　order　estimates　in　a　discrete　H1　norm　for　the　displacement　and　in　H1　and　L2　norms　for　the　pressure.　Finally,　numerical　experiments　are　supplied　to　validate　the　theoretical　error　estimates　of　our　proposed　method.