Fluorescence microscopy is a key driving force behind advances in modern life sciences. However, due to constraints in image formation and acquisition, to obtain high signal-to-noise ratio (SNR) fluorescence images remains difficult. Strong noise negatively affects not only visual observation but also downstream analysis. To address this problem, we propose a blind global noise modeling denoiser (GNMD) that simulates image noise globally using a generative adversarial network (GAN). No prior information on noise properties is required. And no clean training targets need to be provided for noisy inputs. Instead, by simulating real image noise using a GAN, our method synthesizes paired noisy and clean images for training a denoising deep learning network. Experiments on real fluorescence microscopy images show that our method substantially outperforms competing state-of-the-art methods, especially in suppressing background noise. Denoising using our method also facilitates downstream image segmentation.