Based on micromagnetic simulations, we demonstrate nonreciprocal spin-wave transmission in the double-domain wall waveguide within an artificial antiferromagnetic structure. Interestingly, the nonreciprocity of the upper and lower layers is opposite. By bringing the two domain walls closer via an external magnetic field, the resulting dipole interaction causes energy transfer between domain walls. The chirality of the Néel wall in the lower layer is opposite to that of the upper layer, and the Dzyaloshinskii-Moriya interaction at the interface makes the nonreciprocal transmission of the lower layer opposite to that of the upper layer. Changing the frequency of spin waves can adjust the magnitude of the nonreciprocity. Our findings pave the way for the development of novel nonreciprocal magnonic devices.