Aspect-based sentiment analysis (ABSA) is an important subtask of sentiment analysis, which aims to extract the aspects and predict their sentiments. Most existing studies focus on improving the performance of the target domain by fine-tuning domain-specific models (trained on source domains) based on the target domain dataset. Few works propose continual learning tasks for ABSA, which aim to learn the target domain's ability while maintaining the history domains' abilities. In this paper, we propose a Large Language Model-based Continual Learning (\texttt{LLM-CL}) model for ABSA. First, we design a domain knowledge decoupling module to learn a domain-invariant adapter and separate domain-variant adapters dependently with an orthogonal constraint. Then, we introduce a domain knowledge warmup strategy to align the representation between domain-invariant and domain-variant knowledge. In the test phase, we index the corresponding domain-variant knowledge via domain positioning to not require each sample's domain ID. Extensive experiments over 19 datasets indicate that our \texttt{LLM-CL} model obtains new state-of-the-art performance.