Fluorescence microscopy has enabled a dramatic development in modern biology. Due to its inherently weak signal, fluorescence microscopy is not only much noisier than photography, but also presented with Poisson-Gaussian noise where Poisson noise, or shot noise, is the dominating noise source, instead of Gaussian noise that dominates in photography. To get clean fluorescence microscopy images, it is highly desirable to have effective denoising algorithms and datasets that are specifically designed to denoise fluorescence microscopy images. While such algorithms exist, there are no such datasets available. In this paper, we fill this gap by constructing a dataset - the Fluorescence Microscopy Denoising (FMD) dataset - that is dedicated to Poisson-Gaussian denoising. The dataset consists 12,000 real fluorescence microscopy images obtained with commercial confocal, two-photon, and wide-field microscopes and representative biological samples such as cells, zebrafish, and mouse brain tissues. We use imaging averaging to effectively obtain ground truth images and 60,000 noisy images with different noise levels. We use this dataset to benchmark 10 representative denoising algorithms and find that deep learning methods have the best performance. To our knowledge, this is the first microscopy image dataset for Poisson-Gaussian denoising purposes and it could be an important tool for high-quality, real-time denoising applications in biomedical research.