The low-temperature thermal conductivity of suspended long and narrow graphene ribbon with domain walls is investigated. Three acoustic phonon branches and the torsion mode are taken into account. The influence of domain walls replaces the low-temperature “quantum wire” behaviour of thermal conductivity κ ∼ T with Tn behaviour, where n < 1. The transition from “quantum-wire” to “2D graphene”-like behaviour is shifted to the higher temperature when domain walls are present.