An alteative approach is proposed to realize an n-qubit Toffoli gate with superconducting quantum-interference devices (SQUIDs) in cavity quantum electrodynamics (QED). In the proposal, we represent two logical gates of a qubit with the two lowest levels of a SQUID while a higher-energy intermediate level of each SQUID is utilized for the gate manipulation. During the operating process, because the cavity field is always in vacuum state, the requirement on the cavity is greatly loosened and there is no transfer of quantum information between the cavity and SQUIDs.