We propose a scheme to implement the n-qubit Deutsch-Jozsa algorithm based on resonant interaction between the atoms and a single-mode cavity. In the scheme, the resonant transitions between two ground states and one excited state of an atom are changed alteately by adjusting the cavity frequency appropriately, and the operations required to complete the algorithm can be significantly simplified following the increment of the number of qubits. The implementation of the scheme in experiment would show the full power of quantum algorithm and would be significative and important for more complicated quantum algorithm in cavity quantum electrodynamics.