Abstract We investigate the thermal conductivity in the armchair and zigzag graphyne nanoribbons by using the nonequilibrium molecular dynamics method. The results show that a strong orientation dependence of the thermal conductivity is observed. The thermal conductivity in the armchair graphyne nanoribbon is larger than that in the zigzag graphyne nanoribbon with the same width and length at room temperature. Furthermore, the orientation dependence is increased when the width of the graphyne nanoribbons decreases. We disclose the underlying mechanism for this intrinsic orientation dependence to be the more phonon transport channels and higher phonon velocity in armchair graphyne nanoribbon throughout the overall frequency range.