Underwater images suffer from localized distortion and blurred degradation of edge structures due to light absorption and scattering by water. However, existing super-resolution (SR) methods for underwater images cannot effectively solve the above problems and encounter model sizes that are too large. To this end, we propose an attention-guided hybrid transformer-CNN network (AHTCN) to improve the SR reconstruction of underwater images through the interaction of local and multiscale global information, as well as the long-range dependencies modeling capability. Specifically, AHTCN mainly consists of several cascaded transformer-CNN feature extraction blocks (TCFEB) and an image reconstruction module. In TCFEB, the designed attention-based channel separation mechanism can adaptively separate the weighted features while reducing the number of model parameters and then extract the local details and global structural information at different scales through the dual-stream structure. Moreover, we replace the feedforward layer in the transformer with the blueprint separable convolutional feedforward layer and propose an enhanced pyramid pooling transformer layer, which helps to strengthen the feature perception of the model. Experimental results demonstrate that AHTCN outperforms the state-of-the-art algorithms in terms of both subjective visual effects and objective quality assessment, while requiring fewer parameters.