Multiple sclerosis (MS) is the most common demyelinating disease. In MS, demyelination occurs in the white matter of the brain and in the spinal cord. It is thus essential to measure the tissue myelin content to understand the physiopathology of MS, track progression and assess treatment efficacy. Positron emission tomography (PET) with [11C]PIB is a reliable method to measure myelin content in vivo. However, the availability of PET in clinical centers is limited. Moreover, it is expensive to acquire and invasive due to the injection of a radioactive tracer. By contrast, MR imaging is non-invasive, less expensive and widely available, but conventional MRI sequences cannot provide a direct and reliable measure of myelin. In this work, we therefore propose, to the best of our knowledge for the first time, a method to predict the PET-derived myelin content map from multimodal MRI. To that purpose, we introduce a new approach called Sketcher-Refiner generative adversarial networks (GANs) with specifically designed adversarial loss functions. The first network (Sketcher) generates global anatomical and physiological information. The second network (Refiner) refines and generates the tissue myelin content. A visual attention saliency map is also proposed to interpret the attention of neural networks. Our approach is shown to outperform the state-of-the-art methods in terms of image quality and myelin content prediction. Particularly, our prediction results show similar results to the PET-derived gold standard at both global and voxel-wise levels indicating the potential for clinical management of patients with MS.