Point of interest auto-completion (POI-AC) is a featured function in the search engine of many Web mapping services. This function keeps suggesting a dynamic list of POIs as a user types each character, and it can dramatically save the effort of typing, which is quite useful on mobile devices. Existing approaches on POI-AC for industrial use mainly adopt various learning to rank (LTR) models with handcrafted features and even historically clicked POIs are taken into account for personalization. However, these prior arts tend to reach performance bottlenecks as both heuristic features and search history of users cannot directly model personal input habits. In this paper, we present an end-to-end neural-based framework for POI-AC, which has been recently deployed in the search engine of Baidu Maps, one of the largest Web mapping applications with hundreds of millions monthly active users worldwide. In order to establish connections among users, their personal input habits, and correspondingly interested POIs, the proposed framework (abbr. P3AC) is composed of three components, i.e., a multi-layer Bi-LSTM network to adapt to personalized prefixes, a CNN-based network to model multi-sourced information on POIs, and a triplet ranking loss function to optimize both personalized prefix embeddings and distributed representations of POIs. We first use large-scale real-world search logs of Baidu Maps to assess the performance of P3AC offline measured by multiple metrics, including Mean Reciprocal Rank (MRR), Success Rate (SR), and normalized Discounted Cumulative Gain (nDCG). Extensive experimental results demonstrate that it can achieve substantial improvements. Then we decide to launch it online and observe that some other critical indicators on user satisfaction, such as the average number of keystrokes and the average typing speed at keystrokes in a POI-AC session, which significantly decrease as well. In addition, we have released both the source codes of P3AC and the experimental data to the public for reproducibility tests.