This work is devoted to overcome the locking phenomenon for the Biot-Brinkman model, which describes the interaction between the deformation of a fluid-saturated porous medium and viscous fluid flow. By introducing the total pressure in the Biot-Brinkman equations, a four-field formulation is derived as the target model. Well-posedness is followed independent of the material parameters. The mixed interior penalty discontinuous Galerkin (IPDG) methods are used to derive stable numerical solutions. Error estimates in both $$$ {L}^2 $$$–norm and energy norm are established, which show optimum for the SIPG scheme, and achieve parameter robustness in the case of $$$ \lambda \to \infty $$$. Numerical examples are provided to verify the accuracy and stability, as well as locking-free of the proposed mixed DG methods.