Group fairness is important to consider in tensor decomposition to prevent discrimination based on social grounds such as gender or age. Although few works have studied group fairness in tensor decomposition, they suffer from performance degradation. To address this, we propose STAFF (Sparse Tensor Augmentation For Fairness) to improve group fairness by minimizing the gap in completion errors of different groups while reducing the overall tensor completion error. Our main idea is to augment a tensor with augmented entities including sufficient observed entries to mitigate imbalance and group bias in the sparse tensor. We evaluate STAFF on tensor completion with various datasets under conventional and deep learning-based tensor models. STAFF consistently shows the best trade-off between completion error and group fairness; at most, it yields \(36 \%\) lower MSE and \(59 \%\) lower MADE than the second-best baseline.