Super-resolution optical imaging is crucial to the study of cellular processes. Current super-resolution fluorescence microscopy is restricted by the need of special fluorophores or sophisticated optical systems, or long acquisition and computational times. In this work, we present a deep-learning-based super-resolution technique of confocal microscopy. We devise a two-channel attention network (TCAN), which takes advantage of both spatial representations and frequency contents to learn a more precise mapping from low-resolution images to high-resolution ones. This scheme is robust against changes in the pixel size and the imaging setup, enabling the optimal model to generalize to different fluorescence microscopy modalities unseen in the training set. Our algorithm is validated on diverse biological structures and dual-color confocal images of actin-microtubules, improving the resolution from ~ 230 nm to ~ 110 nm. Last but not least, we demonstrate live-cell super-resolution imaging by revealing the detailed structures and dynamic instability of microtubules.