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Quantization approximates a deep network model with floating-point numbers by the one with low bit width numbers, in order to accelerate inference and reduce computation. Quantizing a model without access to the original data, zero-shot quantization can be accomplished by fitting the real data distribution by data synthesis. However, zero-shot quantization achieves inferior performance compared to the post-training quantization with real data. We find it is because: 1) a normal generator is hard to obtain high diversity of synthetic data, since it lacks long-range information to allocate attention to global features; 2) the synthetic images aim to simulate the statistics of real data, which leads to weak intra-class heterogeneity and limited feature richness. To overcome these problems, we propose a novel deep network quantizer, dubbed Long-Range Zero-Shot Generative Deep Network Quantization (LRQ). Technically, we propose a long-range generator to learn long-range information instead of simple local features. In order for the synthetic data to contain more global features, long-range attention using large kernel convolution is incorporated into the generator. In addition, we also present an Adversarial Margin Add (AMA) module to force intra-class angular enlargement between feature vector and class center. As AMA increases the convergence difficulty of the loss function, which is opposite to the training objective of the original loss function, it forms an adversarial process. Furthermore, in order to transfer knowledge from the full-precision network, we also utilize a decoupled knowledge distillation. Extensive experiments demonstrate that LRQ obtains better performance than other competitors.