Federated Learning (FL) provides a promising distributed learning paradigm, since it seeks to protect users privacy by not sharing their private training data. Recent research has demonstrated, however, that FL is susceptible to model inversion attacks, which can reconstruct users' private data by eavesdropping on shared gradients. Existing defense solutions cannot survive stronger attacks and exhibit a poor trade-off between privacy and performance. In this paper, we present a straightforward yet effective defense strategy based on obfuscating the gradients of sensitive data with concealing data. Specifically, we alter a few samples within a mini batch to mimic the sensitive data at the gradient levels. Using a gradient projection technique, our method seeks to obscure sensitive data without sacrificing FL performance. Our extensive evaluations demonstrate that, compared to other defenses, our technique offers the highest level of protection while preserving FL performance. Our source code is located in the repository.