Incremental learning enables continuous model adaptation based on a constantly arriving data stream. It is a way relevant to human cognitive system, which learns to predict objects in a changing world. Incremental learning for character recognition is a typical scenario that characters appear sequentially and the font/writing style changes irregularly. In the paper, we investigate how to classify characters incrementally (i.e., input patterns appear once at a time). A reasonable assumption is that adjacent characters from the same font or the same writer share the same style in a short period while style variation occurs in characters printed by different fonts or written by different persons during a long period. The challenging issue here is how to take advantage of the local style consistency and adapt to the continuous style variation as well incrementally. For this purpose, we propose a continuous incremental adaptive learning vector quantization (CIALVQ) method, which incrementally learns a self-adaptive style transfer matrix for mapping input patterns from style-conscious space onto style-free space. After style transformation, this problem is casted into a common character recognition task and an incremental learning vector quantization (ILVQ) classifier is used. In this framework, we consider two learning modes: supervised incremental learning and active incremental learning. In the latter mode, samples receiving low confidence from the classifier are requested class labels. We evaluated the classification performance of CIALVQ in two scenarios, interleaved test-then-train and style-specific classification on NIST hand-printed data sets. The results show that local style consistency improves the accuracies of both two test scenarios, and for both supervised and active incremental learning modes.