As a fine-grained sentiment analysis method, aspect-based sentiment analysis is playing an increasingly important role in many application scenarios. However, with the ubiquity of social media and online reviews, cross-domain aspect-based sentiment analysis faces two major challenges: insufficient labeled data in the target domain and textual distribution differences between the source and target domains. Currently, many data augmentation methods attempt to alleviate these issues, yet the target domain text generated by these methods often suffers from shortcomings such as lack of fluency, limited diversity of generated data, and convergent source domain. To address these issues, this study proposes a method for cross-domain aspect-based sentiment analysis based on data augmentation from a large language model (LLM). This method leverages the rich language knowledge of large language models to construct appropriate prompts for the cross-domain aspect-based sentiment analysis task. It mines similar texts between the target domain and the source domain and uses context learning to guide the LLM to generate labeled text data in the target domain with domain-associated keywords. This approach addresses the lack of data in the target domain and the domain-specificity problem, effectively improving the accuracy and robustness of cross-domain sentiment analysis. Experiments on multiple real datasets show that the proposed method can effectively enhance the performance of the baseline model in cross-domain aspect-based sentiment analysis.