The sentiment classification aims to learn sentiment features from the annotated corpus and automatically predict the sentiment polarity of new sentiment text. However, people have different ways of expressing feelings in different domains. Thus, there are important differences in the characteristics of sentimental distribution across different domains. At the same time, in certain specific domains, due to the high cost of corpus collection, there is no annotated corpus available for the classification of sentiment. Therefore, it is necessary to leverage or reuse existing annotated corpus for training. In this article, we proposed a new algorithm for extracting central sentiment sentences in product reviews, and improved the pre-trained language model Bidirectional Encoder Representations from Transformers (BERT) to achieve the domain transfer for cross-domain sentiment classification. We used various pre-training language models to prove the effectiveness of the newly proposed joint algorithm for text-ranking and emotional words extraction, and utilised Amazon product reviews data set to demonstrate the effectiveness of our proposed domain-transfer framework. The experimental results of 12 different cross-domain pairs showed that the new cross-domain classification method was significantly better than several popular cross-domain sentiment classification methods.