A scheme for preparing three-atom W state via nonresonant interaction between Ξ-type three-level Rydberg atoms and a single-mode cavity in cavity quantum electrodynamics (QED) is proposed. The scheme requires three three-level atoms and one single-mode cavity. The cavity field is initially in the vacuum state, the first and second atoms interacting with the cavity are initially in the excited state, while the third atom is in the ground state. The practical feasibility of the scheme and the influence of detuning δ on fidelity are analyzed and discussed. Numerical calculation demonstrates that the fidelity and the corresponding success probability of the entangled state is different when the atom-field interaction time is different, and W states with maximized fidelity can be obtained by choosing the appropriate interaction time. It is also shown that in the case of different coupling constants, the effect of detuning δ on fidelity is different. According to this work, it is shown that the scheme can be generalized to prepare W state with arbitrary weight.