Although numerous studies have been conducted on cuffless blood pressure (BP) estimation using machine learning methods, most of the data-driven models are static, with model parameters fixed after training is complete. However, BP is dynamic and the performance would degrade for a static model when the to-be predicted BP distribution deviates from the training BP distribution. In this paper, we propose a continual learning (CL) framework in which deep learning models are developed to learn dynamically and continuously for arterial BP (ABP) estimation with photoplethysmography (PPG) and electrocardiogram (ECG) waveforms. The effectiveness of the CL model is validated on UCI Repository and MIMIC-III database with a total of 132 individual samples, and compared with conventional training method. It was found that the CL model improved the ABP estimation accuracy in terms of mean absolute error (MAE) by 17.47% on average compared with conventional training model. Furthermore, the improvement increased with the variability of ABP. These results demonstrate that CL model has potential to estimate dynamic ABP, which has been challenging with conventional training.