Recently, a new form of online shopping becomes more and more popular, which combines live streaming with E-Commerce activity. The streamers introduce products and interact with their audiences, and hence greatly improve the performance of selling products. Despite of the successful applications in industries, the live stream E-commerce has not been well studied in the data science community. To fill this gap, we investigate this brand-new scenario and collect a real-world Live Stream E-Commerce (LSEC) dataset. Different from conventional E-commerce activities, the streamers play a pivotal role in the LSEC events. Hence, the key is to make full use of rich interaction information among streamers, users, and products. We first conduct data analysis on the tripartite interaction data and quantify the streamers influence on users purchase behavior. Based on the analysis results, we model the tripartite information as a heterogeneous graph, which can be decomposed to multiple bipartite graphs in order to better capture the influence. We propose a novel Live Stream E-Commerce Graph Neural Network framework (LSEC-GNN) to learn the node representations of each bipartite graph, and further design a multi-task learning approach to improve product recommendation. Extensive experiments on two real-world datasets with different scales show that our method can significantly outperform various baseline approaches.