Structured illumination microscopy (SIM) is an important super-resolution based microscopy technique that breaks the diffraction limit and enhances optical microscopy systems. With the development of biology and medical engineering, there is a high demand for real-time and robust SIM imaging under extreme low light and short exposure environments. Existing SIM techniques typically require multiple structured illumination frames to produce a high-resolution image. In this paper, we propose a single-frame structured illumination microscopy (SF-SIM) based on deep learning. Our SF-SIM only needs one shot of a structured illumination frame and generates similar results compared with the traditional SIM systems that typically require 15 shots. In our SF-SIM, we propose a noise estimator which can effectively suppress the noise in the image and enable our method to work under the low light and short exposure environment, without the need for stacking multiple frames for non-local denoising. We also design a bandpass attention module that makes our deep network more sensitive to the change of frequency and enhances the imaging quality. Our proposed SF-SIM is almost 14 times faster than traditional SIM methods when achieving similar results. Therefore, our method is significantly valuable for the development of microbiology and medicine.