The physical ocean phenomena in the ocean affect the changes of water body, which has an important influence on the sound propagation. A hyperbolic frequency modulation (HFM) signal sound propagation experiment of towed sound source in the East Indian Ocean (EIO) was conducted in summer 2019. The center frequency of the towed sound source is 300 Hz, and the hydrophone receives the data from 4130 m far. This is the first time that we have conducted the underwater acoustic survey in the Indian Ocean. The influence of the physical ocean phenomenon—Indian Ocean Dipole (IOD) on sound propagation is observed. The experimental data of sound propagation from the IOD are processed and analyzed, the effects of sound source depth and water fluctuation on the deep-sea convergence zone (CZ) are analyzed, and the formation mechanism of sound propagation phenomenon in the experiment is explained theoretically. The results show that the second CZ is not formed under the influence of the warm water mass formed by the IOD and the depth of the sound source in the incomplete deep channel environment of the EIO. Owing to the fluctuation of the sound source depth, the deep-sea CZ disappears at the distance where it should have appeared. When the depth of the sound source becomes deeper, it is easier to form the deep-sea CZ. Under the influence of the IOD, the thermocline fluctuation at the location of the second CZ has an important influence on the formation and location of the third CZ. It is found that the location of the third CZ shifts 2–3 km toward the sound source in the experiment. The research results have important significance in guiding the applications in detection and communication sonar in deep-sea complex environment.