In this work we focus on fine-tuning a pre-trained BERT model and applying it to patent classification. When applied to large datasets of over two millions patents, our approach outperforms the state of the art by an approach using CNN with word embeddings. In addition, we focus on patent claims without other parts in patent documents. Our contributions include: (1) a new state-of-the-art method based on pre-trained BERT model and fine-tuning for patent classification, (2) a large dataset USPTO-3M at the CPC subclass level with SQL statements that can be used by future researchers, (3) showing that patent claims alone are sufficient for classification task, in contrast to conventional wisdom.