Pre-training models on Imagenet or other massive datasets of real images has led to major advances in Computer vision, albeit accompanied with shortcomings related to curation cost, privacy, usage rights, and ethical issues. In this paper, for the first time, we study the transferability of pre-trained models based on synthetic data generated by graphics simulators to downstream tasks from very different domains. In using such synthetic data for pre-training, we find that downstream performance on different tasks are fa-vored by different configurations of simulation parameters (e.g. lighting, object pose, backgrounds, etc.), and that there is no one-size-fits-all solution. It is thus better to tailor syn-thetic pre-training data to a specific downstream task, for best performance. We introduce Task2Sim, a unified model mapping downstream task representations to optimal sim-ulation parameters to generate synthetic pre-training data for them. Task2Sim learns this mapping by training to find the set of best parameters on a set of 'seen' tasks. Once trained, it can then be used to predict best simulation pa-rameters for novel 'unseen' tasks in one shot, without re-quiring additional training. Given a budget in number of images per class, our extensive experiments with 20 di-verse downstream tasks show Task2Sim's task-adaptive pre-training data results in significantly better downstream per-formance than non-adaptively choosing simulation param-eters on both seen and unseen tasks. It is even competitive with pre-training on real images from Imagenet.