Nanorobots have been used in smart health to collect time series data such as electrocardiograms and electroencephalograms. Real-time classification of dynamic time series signals in nanorobots is a challenging task. Nanorobots in the nanoscale range require a classification algorithm with low computational complexity. First, the classification algorithm should be able to dynamically analyze time series signals and update itself to process the concept drifts (CD). Second, the classification algorithm should have the ability to handle catastrophic forgetting (CF) and classify historical data. Most importantly, the classification algorithm should be energy-efficient to use less computing power and memory to classify signals in real-time on a smart nanorobot. To solve these challenges, we design an algorithm that can Prevent Concept Drift in Online continual Learning for time series classification (PCDOL). The prototype suppression item in PCDOL can reduce the impact caused by CD. It also solves the CF problem through the replay feature. The computation per second and the memory consumed by PCDOL are only 3.572M and 1KB, respectively. The experimental results show that PCDOL is better than several state-of-the-art methods for dealing with CD and CF in energy-efficient nanorobots.