Urban power grids have high load densities and are subjected to many critical loads. Improving the extreme survival capacity of an urban power grid under extreme conditions and events help to ensure uninterrupted power supply for important users, improve the anti-vulnerability capacity of the power grid, and reduce the impact and losses caused by extreme events. In this study, an anti-fragile planning method for a large-scale urban distribution network is developed to improve the extreme survival capacity. First, a two-step decision-making framework for urban distribution network resilience planning based on the stochastic programming theory is proposed. The first step of the framework is to determine the set of candidate line reinforcement/upgrading schemes, and the second step is to determine the optimal deployment scheme of distributed power sources in the line-planning scheme based on the stochastic programming theory. The final resilience planning scheme is determined by considering factors, such as investment economy and extreme survival capacity improvement effect. Among different candidate line reinforcement/upgrading schemes, an extreme scene generation and representative scene-screening method based on Monte Carlo simulation and K-means clustering is proposed, considering the possible typhoon extreme disasters. Next, the planning problem of distributed generation is constructed as a two-stage random mixed-integer programming to optimize investment economy and maximize extreme survival capacity, and the random programming problem is transformed into a deterministic mixed-integer linear-programming problem based on the above extreme scenarios. The IEEE 33-node and 123-node distribution systems are used to verify the effectiveness of the proposed method.