This paper presents a thorough approach characterizing the spiraling motion of underwater gliders. The dynamic model for underwater gliders, steered by a single internal movable and rotatable mass, is established. Spiraling motions are equilibria of the dynamics, for which equations are derived and then solved by a recursive algorithm with fast convergence. This theoretical method is applied to the Seawing underwater glider whose hydrodynamic coefficients are computed using computational fluid dynamics (CFD) software packages. In a recent experiment in the South China Sea, the Seawing glider produced a spiraling motion against strong ocean current, agreeing with theoretical predictions. Hence the recursive algorithm may be used to compute control input to achieve desired spiraling motion for underwater gliders in practice.