We　propose　a　symmetric　interior　penalty　discontinuous　Galerkin　(DG)　method　for　nonlinear　fully　coupled　quasi-static　thermo-poroelasticity　problems.　Firstly,　a　fully　implicit　nonlinear　discrete　scheme　is　constructed　by　adopting　the　DG　method　for　the　spatial　approximation　and　the　backward　Euler　method　for　the　temporal　discretization.　Subsequently,　the　existence　and　uniqueness　of　the　solution　of　the　numerical　scheme　is　proved,　and　then　we　derive　the　a　priori　error　estimate　for　the　three　variables,　i.e.,　the　displacement,　the　pressure　and　the　temperature.　Lastly,　we　carry　out　numerical　experiments　to　confirm　the　theoretical　findings　of　our　suggested　approach.