A　two-way　full-duplex　multiple-input　multiple-output　(MIMO)　relay　provides　effective　spectral　efficiency　and　system　capacity　improvement.　However,　self-interference　(SI)　as　a　serious　problem　limits　the　development　of　a　full-duplex　relay.　In　this　paper,　the　novel　SI　suppression　schemes　based　on　the　Dempster-Shafer　(DS)　evidence　theory　are　proposed　to　suppress　SI　in　the　two-way　full-duplex　MIMO　relay.　DS　evidence　theory　can　appropriately　characterize　uncertainty　and　make　full　use　of　multiple　evidence　source　information　by　DS　combination　rule　to　obtain　reliable　decisions.　The　first　proposed　DS　network　coding　(DS-NC)　scheme　adopts　DS　evidence　theory　to　detect　the　signal　of　each　source　node,　considering　SI　suppression　in　the　basic　probability　assignment　computation　in　the　multiple　access　phase.　Moreover,　different　from　the　DS-NC　scheme,　the　further　proposed　DS　physical-layer　network　coding　(DS-PNC)　scheme　considers　SI　suppression　from　the　vector　space　perspective　and　combines　the　PNC　mapping　rule　with　the　DS　theory　to　obtain　a　network-coded　signal　without　estimating　each　source　node　signal.　In　the　broadcast　phase,　antenna　selection　is　adopted　at　the　relay　and　DS　evidence　theory　is　also　applied　at　each　source　node　for　SI　suppression.　Meanwhile,　the　effects　of　imperfect　SI　channel　estimation　and　the　intended　channel　estimation　on　the　proposed　schemes　are　also　studied.　Finally,　the　proposed　DS-PNC　scheme　is　studied　with　the　SI　signal　model　which　considers　analog　radio　frequency　cancellation,　the　effects　of　I/Q　modulator　imbalances,　and　power　amplifier　nonlinearity　of　the　transmitter.　Simulation　results　reveal　that　the　proposed　DS-PNC　scheme　is　a　little　more　sensitive　to　the　channel　estimation　errors　than　the　traditional　spatial-domain　schemes.　However,　with　the　perfect　channel　state　information,　the　proposed　DS-NC　with　one　iteration　and　DS-PNC　schemes　outperform　traditional　spatial-domain　schemes.　Furthermore,　considering　the　SI　signal　model　with　nonlinear　distortion　and　radio　frequency　cancellation,　the　DS-PNC　scheme　is　also　superior　to　the　traditional　schemes.　Meanwhile,　the　DS-PNC　scheme　is　more　robust　to　the　SI　and　achieves　the　same　diversity　gain　as　the　ideal　cancellation.