Without sufficient preparation and on-site management, the mass scale unexpected huge human crowd is a serious threat to public safety. A recent impressive tragedy is the 2014 Shanghai Stampede, where 36 people were killed and 49 were injured in celebration of the New Year's Eve on December 31th 2014 in the Shanghai Bund. Due to the innately stochastic and complicated individual movement, it is not easy to predict collective gatherings, which potentially leads to crowd events. In this paper, with leveraging the big data generated on Baidu map, we propose a novel approach to early warning such potential crowd disasters, which has profound public benefits. An insightful observation is that, with the prevalence and convenience of mobile map service, users usually search on the Baidu map to plan a routine. Therefore, aggregating users' query data on Baidu map can obtain priori and indication information for estimating future human population in a specific area ahead of time. Our careful analysis and deep investigation on the Baidu map data on various events also demonstrates a strong correlation pattern between the number of map query and the number of positioning users in an area. Based on such observation, we propose a decision method utilizing query data on Baidu map to invoke warnings for potential crowd events about 1-3 hours in advance. Then we also construct a machine learning model with heterogeneous data (such as query data and mobile positioning data) to quantitatively measure the risk of the potential crowd disasters. We evaluate the effectiveness of our methods on the data of Baidu map.