To realize practical application, the attenuation of spin waves because of boundary scattering and multimode dispersion in magnonic waveguides must be greatly reduced. Up to now, there have been not good solutions to this problem. Here, we propose and demonstrate by micromagnetic simulations to use the longitudinal chiral domain wall imprinted into a waveguide with the interfacial Dzyaloshinskii–Moriya interaction (DMI) to introduce a deep potential well and guide spin waves forming an ultra narrow internal spin-wave channel (~10 nm). Spin waves along this channel can prevent scattering arising from boundary roughness and multimode coexistence and thus should exhibit reduced attenuation and enhanced coherence, which is highly desired in building real spin-wave devices. Moreover, we show that the spin-wave transmission in this waveguide with the DMI can be switched on and off at the frequencies lower than a threshold frequency f2 by changing the static domain state. This property is explored to construct logical NAND gate by connecting two logical NOT gates in parallel.