Single-image super-resolution (SISR) has achieved significant breakthroughs with the development of deep learning. However, these methods are difficult to be applied in real-world scenarios since they are inevitably accompanied by the problems of computational and memory costs caused by the complex operations. To solve this issue, we propose a Lightweight Bimodal Network (LBNet) for SISR. Specifically, an effective Symmetric CNN is designed for local feature extraction and coarse image reconstruction. Meanwhile, we propose a Recursive Transformer to fully learn the long-term dependence of images thus the global information can be fully used to further refine texture details. Studies show that the hybrid of CNN and Transformer can build a more efficient model. Extensive experiments have proved that our LBNet achieves more prominent performance than other state-of-the-art methods with a relatively low computational cost and memory consumption. The code is available at https://github.com/IVIPLab/LBNet.