Online advertising driven by auctions brings billions of dollars in revenue for social networking services and e-commerce platforms. GSP auction, which is simple and easy to understand for advertisers, has almost become the benchmark for ad auction mechanisms in the industry. However, the allocation stability of GSP depends on the separable CTR assumption, which means that GSP considers neither position-dependent externalities nor ad-dependent externalities in multi-slot scenario, leading to suboptimal performance. Some GSP-based deep auctions (e.g., DeepGSP, DNA) have attempted to upgrade GSP with deep neural networks, while only modeling local externalities and thus still suboptimal. On the other hand, although VCG-based multi-slot auctions (e.g., VCG, WVCG) take externalities into consideration, they lack an efficient balance of both revenue and social welfare. In this paper, we propose a novel auction named Neural Multi-slot Auction (NMA) to tackle the above-mentioned challenges. Specifically, we model the global externalities effectively with a context-aware list-wise prediction module to achieve better performance. We design a list-wise deep rank module to guarantee incentive compatibility in end-to-end learning. Furthermore, we propose an auxiliary loss for social welfare to effectively reduce the decline of social welfare while maximizing revenue. Experiment results on both offline large-scale datasets and online A/B tests demonstrate that NMA obtains higher revenue with balanced social welfare than other existing auction mechanisms (i.e., GSP, DNA, WVCG) in industrial practice, and we have successfully deployed NMA on Meituan food delivery platform.