The input and output of most text generation tasks can be transformed to two sequences of tokens and they can be modeled using sequence-to-sequence learning modeling tools such as Transformers. These models are usually trained by maximizing the likelihood the output text sequence and assumes the input sequence and all gold preceding tokens are given during training, while during inference the model suffers from the exposure bias problem (i.e., it only has access to its previously predicted tokens rather gold tokens during beam search). In this paper, we propose MoCa ({\bf Mo}mentum {\bf Ca}libration) for text generation. MoCa is an online method that dynamically generates slowly evolving (but consistent) samples using a momentum moving average generator with beam search and MoCa learns to align its model scores of these samples with their actual qualities. Experiments on four text generation datasets (i.e., CNN/DailyMail, XSum, SAMSum and Gigaword) show MoCa consistently improves strong pre-trained transformers using vanilla fine-tuning and we achieve the state-of-the-art results on CNN/DailyMail and SAMSum datasets.