Knowledge distillation has been widely used to produce portable and efficient neural networks which can be well applied on edge devices for computer vision tasks. However, almost all top-performing knowledge distillation methods need to access the original training data, which usually has a huge size and is often unavailable. To tackle this problem, we propose a novel data-free approach in this paper, named Dual Discriminator Adversarial Distillation (DDAD) to distill a neural network without any training data or meta-data. To be specific, we use a generator to create samples through dual discriminator adversarial distillation, which mimics the original training data. The generator not only uses the pre-trained teachers intrinsic statistics in existing batch normalization layers but also obtains the maximum discrepancy from the student model. Then the generated samples are used to train the compact student network under the supervision of the teacher. The proposed method obtains an efficient student network which closely approximates its teacher network, despite using no original training data. Extensive experiments are conducted to to demonstrate the effectiveness of the proposed approach on CIFAR-10, CIFAR-100 and Caltech101 datasets for classification tasks. Moreover, we extend our method to semantic segmentation tasks on several public datasets such as CamVid and NYUv2. All experiments show that our method outperforms all baselines for data-free knowledge distillation.