In pyrochlore iridates, nontrivial magnetic domain walls (DWs) carrying ferromagnetic (FM) moments were recently uncovered despite their bulk all-in-all-out (AIAO) antiferromagnetic (AFM) configurations. Here, we report a field (H) inversion asymmetric behavior of isothermal magnetization M(H) and magnetotransport in pyrochlore Eu 2 Ir 2 O 7 single crystals, which is closely related to the exchange coupling between AIAO AFM domains and FM DWs. After field cooling (FC) below Neeĺ temperature (T N ), a non-zero exchange bias (EB) effect is manifested in the isothermal M(H) curves by the presence of EB field (H EB ) and vertical magnetization shift (M shift ), as well as the shift of both longitudinal [ρ xx (H)] and Hall resistivities [ρ xy (H)] along the FC directions as observed in conventional FM/AFM systems. Moreover, the hysteresis behaviors observed in asymmetric ρ xx (H) and ρ xy (H) reveal the existence of electrical response from frozen FM uncompensated moments, which are produced at the FM DWs due to the interfacial exchange coupling between AIAO domains and FM DWs during the FC procedure.