In online handwritten Chinese text recognition (OHCTR), similar characters are one of the main causes of accuracy degradation. Exploring semantic relationships between characters and applying feature-specific weighting are effective approaches to distinguishing such similar characters. To this end, this paper proposes a hybrid attention network (HAN) to further enhance recognition accuracy. The HAN comprises a semantic attention module (SAM) and a channel attention module (CAM). The SAM captures multi-level semantic relationships among characters within a text line, while the CAM performs weighting across convolutional channels. Compared with the multi-head self attention, the SAM is nonlinear and achieves higher recognition accuracy with lower memory consumption and faster computation speed. Experiments on three publicly available online handwritten Chinese text datasets demonstrate that the proposed HAN outperforms the multi-head attention mechanism. When combined with an end-to-end convolutional recurrent network, the HAN achieves excellent recognition performance on OHCTR.