Segmentation-based handwritten text recognition has the advantage of character interpretability but needs a character classifier with high classification accuracy and non-character rejection capability. The classifier can be trained on both character samples and string samples but real string samples are usually insufficient. In this paper, we proposed a learning method for segmentation-based online handwritten Chinese text recognition with a convolutional prototype network as the underlying classifier. The prototype classifier is inherently resistant to non-characters, and so, can be trained with character and string samples without the need of data augmentation. The learning has two stages: pre-training on character samples with a modified loss function for improving non-character resistance, and weakly supervised learning on both character and string samples for improving recognition performance. Experimental results on the CASIA-OLHWDB and ICDAR2013-Online datasets show that the proposed method can achieve promising recognition performance without training data augmentation.