This study draws inspiration from the locomotion and adaptability of aquatic snakes to develop an innovative soft-bodied, hydraulic-driven untethered underwater snake robot “BaiLong.” The robot consists of a segmented soft structure and embeds actuation, control, and power modules in the head. Featuring the self-shape perception capability, it leverages an online iterative learning control method to effectively mitigate body shape deformation errors and attain precise gait movements. As a result, the soft robot has achieved movements emulating the serpentine motion of real snakes with locomotion consistency equivalent to rigid robots. Extensive experiments in both artificial and natural aquatic environments have presented improved swimming speed among soft snakes with promising turning agility, and revealed the gait parameter influence on the linear velocity described by a near-constant Strouhal number. The reported investigation sufficiently demonstrates the swimming feasibility and performance of underwater soft snake robots and significantly advances their capabilities for long-range applications.