Acoustic propagation in horizontally varying double duct waveguides under ice cover was investigated for the phenomenon of double duct waveguides in some Arctic seas. The ice reflection coefficients on the rough undersurface were derived and determined by the perturbation method, and the acoustic propagation characteristics of the horizontally varying double duct waveguide in the measured sea area were computed and analyzed by combining with the Bellhop ray model, and the influences of the depth of the sound source, the angle of incidence of the sound source and the frequency of the sound source on the acoustic propagation in the horizontally varying double duct waveguide were also investigated. The results show that in the Arctic, acoustic propagation in the deep-sea sound duct is mostly confined to the upper and lower edges of the deep-sea sound duct; the acoustic propagation loss is smaller when the sound source is at the same depth as the horizontally varying deep-sea sound duct axis, and the horizontally varying sound velocity profile has a lower acoustic propagation loss compared to the horizontally unchanged one when the sound source is located outside of the boundary of the deep-sea sound duct; the angle of incidence has a smaller effect on the acoustic propagation in the double duct waveguide; as the frequency of the sound source increases, the acoustic propagation loss in the surface duct increases, but the effect on the deep-sea duct is not obvious, and the horizontally varying sound velocity profile is more favorable for acoustic propagation at the same frequency.