In optimization of a shared autonomous electric vehicle (SAEV) system, idle vehicle relocation strategies are important to reduce operation costs and customers’ wait time. However, for an on-demand service, continuous optimization for idle vehicle relocation is computationally expensive, and thus, not effective. This study proposes a deep learning-based algorithm that can instantly predict the optimal solution to idle vehicle relocation problems under various traffic conditions. The proposed relocation process comprises three steps. First, a deep learning-based passenger demand prediction model using taxi big data is built. Second, idle vehicle relocation problems are solved based on predicted demands, and optimal solution data are collected. Finally, a deep learning model using the optimal solution data is built to estimate the optimal strategy without solving relocation. In addition, the proposed idle vehicle relocation model is validated by applying it to optimize the SAEV system. We present an optimal service system including the design of SAEV vehicles and charging stations. Further, we demonstrate that the proposed strategy can drastically reduce operation costs and wait times for on-demand services.