We propose a scheme to implement the Deutsch-Jozsa algorithm by using Schr(o)dinger cat states in cavity quantum electron-dynamics (QED). The scheme is based on the Raman interaction of a degenerate three-level A-type atom with a coherent state in a cavity. By using Schr(o)dinger cat states, the atomic spontaneous emission can be minimized and the Hadamard transformation in our scheme is not needed.