As a critical structure in ship and marine engineering, axially moving shape-memory alloy (SMA) plates may exhibit complex dynamic behaviors. However, there are few studies investigating the dynamic response of SMA plates under underwater blast, let alone consider the effect of initial geometric imperfection and axial motion. Therefore, further studies on such topic are warranted. Based on this, the current paper dedicates to conducting the dynamic research of the geometrically imperfect SMA plate subjected to underwater blast. Firstly, adopting Falk's polynomial constitutive model, the stress strain constitutive relationship of SMA plate can be determined. Secondly, the Hamilton's principle is employed to derive the vibration equation. Thirdly, the assumed mode method and Runge-Kutta technique are applied for solving the dynamic system. After that, several comparative analyses are performed. Finally, the influences of immersed depth, axially moving velocity, initial geometric imperfection, elastic foundation, pulse load type, aspect ratio, length-to-thickness ratio, as well as blast loading parameter on the transient response path are discussed. These findings can contribute to understanding the dynamic behavior of the geometrically imperfect SMA plates immersed in water when subjected to blast loading, and thus providing valuable thinking for the manufacturing and design of submarine equipment.