Short-term traffic speed prediction has been an important research topic in the past decade, and many approaches have been introduced. However, providing fine-grained, accurate, and efficient traffic-speed prediction for large-scale transportation networks where numerous traffic detectors are deployed has not been well studied. In this paper, we propose DistPre, which is a distributed fine-grained traffic speed prediction scheme for large-scale transportation networks. To achieve fine-grained and accurate traffic-speed prediction, DistPre customizes a Long Short-Term Memory (LSTM) model with an appropriate hyperparameter configuration for a detector. To make such a customization process efficient and applicable for large-scale transportation networks, DistPre conducts LSTM customization on a cluster of computation nodes and allows any trained LSTM model to be shared between different detectors. If a detector observes a similar traffic pattern to another one, DistPre directly shares the existing LSTM model between the two detectors rather than customizing an LSTM model per detector. Experiments based on traffic data collected from freeway I5-N in California are conducted to evaluate the performance of DistPre. The results demonstrate that DistPre provides time-efficient LSTM customization and accurate fine-grained traffic-speed prediction for large-scale transportation networks.