The security of SHA-3 against different kinds of attacks are of vital importance for crypto systems with SHA-3 as the security engine. In this paper, we look into the differential fault analysis of SHA-3, and this is the first work to conquer SHA3-224 and SHA3-256 using differential fault analysis. Comparing with one existing related work, we relax the fault models and make them realistic for different implementation architectures. We analyze fault propagation in SHA-3 under such single-byte fault models, and propose to use fault signatures at the observed output for analysis and secret retrieval. Results show that the proposed method can effectively identify the injected single-byte faults, and then recover the whole internal state of the input of last round χ operation (χ22i) for both SHA3-224 and SHA3-256.