The sharing economy has offered new viable approaches for firms to tackle demand surges. In this paper, we study a novel network design problem for the fourth-party logistics network (4PLN) to cope with unpredictable demand surges, in which temporary renting of logistics resources from a sharing market is available to supplement network capacity. A chance-constrained stochastic programming model is established to minimize the overall cost for 4PLN under service level targets. To deal with the difficulties brought by the evaluation of service level, we reformulate a mixed-integer linear programming (MILP) model, that can be solved straightly, based on the sample average approximation method. Then, to address the enormous challenge posed by the coupling of the basic NP-hard network design problem and the large number of demand scenarios in the MILP version, the Scenario-Price based Decomposition Algorithm (P-DA) is designed based on the key idea of decomposing the above-coupled factors. Further, to mitigate the performance deterioration brought on by large system scale and/or sample size, we expand our base algorithm to the Greedy Scenario-Reduction and Scenario-Price based Decomposition Algorithm (GR&P-DA) through the fast processing of chance constraints by introducing a greedy method. Through computational experiments, we demonstrate the effectiveness of our proposed model and algorithms, and we analyze the impact of various model parameters, including demand level, surge magnitude, surge probability, and rental price of third-party logistics resources, on 4PLN design. Furthermore, our comparative analysis reveals that renting logistics resources to address demand surges can significantly reduce costs and discovers that deploying resources in advance does not always provide an advantage, a temporary “case-by-case” planning approach for renting will give a more cost-saving scheme when surge probability is at a low level as it avoids idle resources by not being stuck with a conservative strategy.