[en] We construct IIA GS superstring action on the ten-dimensional pp-wave background, which arises as the compactification of eleven-dimensional PP-wave geometry along the isometry direction. The background geometry has 24 Killing spinors and among them, 16 components correspond to the non-linearly realized kinematical supersymmetry in the string action. The remaining eight components are linearly realized and shown to be independent of x⁺ coordinate, which is identified with the world-sheet time coordinate of the string action in the light-cone gauge. The resultant dynamical N=(4, 4) supersymmetry is investigated, which is shown to be consistent with the field contents of the action containing two free massive supermultiplets. (author)