This study investigates strategies for solving the system reliability of large three-dimensional jacket structures. These structural systems normally fail as a result of a series of different components failures. The failure characteristics are investigated under various environmental conditions and direction combinations. The β-unzipping technique is adopted to determine critical failure components, and the entire system is simplified as a series-parallel system to approximately evaluate the structural system reliability. However, this approach needs excessive computational effort for searching failure components and failure paths. Based on a trained artificial neural network (ANN), which can be used to approximate the implicit limit-state function of a complicated structure, a new alternative procedure is proposed to improve the efficiency of the system reliability analysis method. The failure probability is calculated through Monte Carlo simulation (MCS) with Latin hypercube sampling (LHS). The features and applicability of the above procedure are discussed and compared using an example jacket platform located in Chengdao Oilfield, Bohai Sea, China. This study provides a reference for the evaluation of the system reliability of jacket structures.