Answering questions about complex situations in videos requires not only capturing of the presence of actors, objects, and their relations, but also the evolution of these relationships over time. A situation hyper-graph is a representation that describes situations as scene sub-graphs for video frames and hyper-edges for connected sub-graphs, and has been proposed to capture all such information in a compact structured form. In this work, we propose an architecture for Video Question Answering (VQA) that enables answering questions related to video content by predicting situation hyper-graphs, coined Situation Hyper-Graph based Video Question Answering (SHG-VQA). To this end, we train a situation hyper-graph decoder to implicitly identify graph representations with actions and object/human-object relationships from the input video clip and to use cross-attention between the predicted situation hyper-graphs and the question embedding to predict the correct answer. The proposed method is trained in an end-to-end manner and optimized by a cross-entropy based VQA loss function and a Hungarian matching loss for the situation graph prediction. The effectiveness of the proposed architecture is extensively evaluated on two challenging benchmarks: AGQA and STAR. Our results show that learning the underlying situation hyper-graphs helps the system to significantly improve its performance for novel challenges of video question answering task.