In this paper, Whittaker modules for the Schrödinger-Witt algebra sv are defined. The Whittaker vectors and the irreducibility of the Whittaker modules are studied. sv has a triangular decomposition according to its Cartan subalgebra h: sv=sv-+h+sv+. For any Lie algebra homomorphism ψ:sv+→C, we can define Whittaker modules of type ψ. When ψ is nonsingular, the Whittaker vectors, the irreducibility, and the classification of Whittaker modules are completely determined. When ψ is singular, by constructing some special Whittaker vectors, we find that the Whittaker modules are all reducible. Moreover, we get some more precise results for special ψ. [ABSTRACT FROM AUTHOR]