A theory scheme was proposed for implementing a Toffoli gate with threelevel structure superconducting quantuminterference devices (SQUID), based on the cavity quantum electrodynamics (CQED). In this proposal, quantum information was encoded into the two lower levels of a SQUID while a higher level serves as the gate manipulation. Applying the coupling of the cavity field with a SQUID, which was driven by a classical microwave pulse to control the evolution of quantum state, the scheme could be extended to achieve Nqubit Toffoli gate. And, the experimental feasibility of Toffoli gate was disscussed, and the total operation time of fourqubit Toffoli gate was computed only 30 nanometers, which was much shorter than the decay time of the cavity mode or the energy relaxation time of the higher level. And the increasing rate of the gate response time became slow with the increase of the qubit number.