Designing an effective relief network can be a practical approach to facilitating the response to natural disasters. In this study, we investigate a three-stage relief network design problem in the context of typhoon disasters considering time-dependent uncertainties simultaneously. The rescue decisions before, during the typhoon warning period, and after the typhoon landfalls are made comprehensively. A novel three-stage nonlinear robust optimization (3NRO) model is then formulated. To make the 3NRO model computationally tractable, we further develop a deterministic equivalent (DE) model. A case study demonstrates the superiority of the proposed model.