Estimating the 6D pose of objects is beneficial for robotics tasks such as transportation, autonomous navigation, manipulation as well as in scenarios beyond robotics like virtual and augmented reality. With respect to single image pose estimation, pose tracking takes into account the temporal information across multiple frames to overcome possible detection inconsistencies and to improve the pose estimation efficiency. In this work, we introduce a novel Deep Neural Network (DNN) called VIPose, that combines inertial and camera data to address the object pose tracking problem in real-time. The key contribution is the design of a novel DNN architecture which fuses visual and inertial features to predict the objects' relative 6D pose between consecutive image frames. The overall 6D pose is then estimated by consecutively combining relative poses. Our approach shows remarkable pose estimation results for heavily occluded objects that are well known to be very challenging to handle by existing state-of-the-art solutions. The effectiveness of the proposed approach is validated on a new dataset called VIYCB with RGB image, IMU data, and accurate 6D pose annotations created by employing an automated labeling technique. The approach presents accuracy performances comparable to state-of-the-art techniques, but with the additional benefit of being real-time.