Object handover is a common human collaboration behavior that attracts attention from researchers in Robotics and Cognitive Science. Though visual perception plays an important role in the object handover task, the whole handover process has been specifically explored. In this work, we propose a novel rich-annotated dataset, H2O, for visual analysis of human-human object handovers. The H2O, which contains 18K video clips involving 15 people who hand over 30 objects to each other, is a multi-purpose benchmark. It can support several vision-based tasks, from which, we specifically provide a baseline method, RGPNet, for a less-explored task named Receiver Grasp Prediction. Extensive experiments show that the RGPNet can produce plausible grasps based on the giver's hand-object states in the pre-handover phase. Besides, we also report the hand and object pose errors with existing baselines and show that the dataset can serve as the video demonstrations for robot imitation learning on the handover task. Dataset, model and code will be made public.