A theory of tapered cooling for fast circulating ion beams in a storage ring is constructed. We describe the fundamentals of this cooling scheme, a scheme that effectively yields both transverse and longitudinal cooling through radial-position-dependent longitudinal momentum cooling, emphasizing that it might be the most promising way to beam crystallization. The cooling rates are analytically evaluated to study the ideal operating condition. We discuss the physical implication of the tapering factor of the cooling force, and show how to determine its optimum value. Molecular dynamics is employed to demonstrate the validity of the present theory.