For the unique dual-channel sound speed profiles of the Canadian Basin and the Chukchi Plateau in the Arctic, based on the propagation characteristics of refracted normal modes under dual-channel sound speed profiles, an inversion method using refracted normal modes for dual-channel sound speed profiles is proposed. This method proposes a dual-parameter representation method for dual-channel sound speed profiles, tailored to the characteristics of dual-channel sound speed profiles. A dispersion structure extraction method is proposed for the dispersion structure characteristics of refracted normal modes under dual-channel sound speed profiles. Combining the parameter representation method of sound speed profiles and the dispersion structure extraction method, an inversion method for dual-channel sound speed profiles is proposed. For the common horizontal variation of sound speed profiles in long-distance acoustic propagation, a method for inverting horizontally varying dual-channel sound speed profiles is proposed. Finally, this article verifies the effectiveness of the dual-channel sound speed profile inversion method using the Arctic low-frequency long-range acoustic propagation experiment. Compared with previous sound speed profile inversion methods, the method proposed in this article has the advantages of fewer inversion parameters and faster inversion speed. It can be implemented using only a single hydrophone passively receiving random air gun signals, and it also solves the inversion problem of horizontal variation of sound speed profiles. It has significant advantages such as low cost, easy deployment, and fast computation speed.