This paper proposes a supervised classification algorithm capable of continual learning by utilizing an Adaptive Resonance Theory (ART)-based growing self-organizing clustering algorithm. The ART-based clustering algorithm is theoretically capable of continual learning, and the proposed algorithm independently applies it to each class of training data for generating classifiers. Whenever an additional training data set from a new class is given, a new ART-based clustering will be defined in a different learning space. Thanks to the above-mentioned features, the proposed algorithm realizes continual learning capability. Simulation experiments showed that the proposed algorithm has superior classification performance compared with state-of-the-art clustering-based classification algorithms capable of continual learning.