Raman imaging (RI) is an outstanding technique that enables molecular-level medical diagnostics and therapy assessment by providing characteristic fingerprint and morphological information about molecules. However, obtaining high-quality Raman images generally requires a long acquisition time, up to hours, which is prohibitive for RI applications of timely cytopathology and histopathology analyses. To address this issue, image super-resolution (SR) based on deep learning, including convolutional neural networks and transformers, has been widely recognized as an effective solution to reduce the time required for achieving high-quality RI. In this study, a locality enhanced transformer network (LETNet) is proposed to perform Raman image SR. Specifically, the general architecture of the transformer is adopted with the replacement of self-attention by convolution to generate high-fidelity and detailed SR images. Additionally, the convolution in the LETNet is further optimized by utilizing depth-wise convolution to improve the computational efficiency of the model. Experiments on hyperspectral Raman images of breast cancer cells and Raman images of a few channels of brain tumor tissues demonstrate that the LETNet achieves superior 2×, 4×, and 8× SR with fewer parameters compared with other SR methods. Consequently, high-quality Raman images can be obtained with a significant reduction in time, ranging from 4 to 64 times. Overall, the proposed method provides a novel, efficient, and reliable solution to expedite high-quality RI and promote its application in real-time diagnosis and therapy.