It has been a common approach to pre-train a language model on a large corpus and fine-tune it on task-specific data. In practice, we observe that fine-tuning a pre-trained model on a small dataset may lead to over- and/or under-estimate problem. In this paper, we propose MC-Tailor, a novel method to alleviate the above issue in text generation tasks by truncating and transferring the probability mass from over-estimated regions to under-estimated ones. Experiments on a variety of text generation datasets show that MC-Tailor consistently and significantly outperforms the fine-tuning approach.