In the era of information overload, various types of information interconnect to form complex networks. To better manage the diffusion paths and ensure that relevant information reaches the appropriate audiences while curbing the spread of less useful content, we propose to predict the transmissibility-the probability of each piece of information being transmitted influenced by other information within the network, which can be applied in recommendation systems and advertising placement. Diverging from existing research that focus on static networks only, our work addresses the more realistic scenario of time-varying networks where the influence strength between related information evolves over time. We propose a novel graph neural network model, Temporal Variation Graph Network (TVGN), to predict the transmissibility by capturing time-varying features and learn the patterns of dynamic diffusion processes. Our proposed model is evaluated on two popular citation networks, Cora [10] and CiteSeer [13]. Our results demonstrate that our model achieves low estimation error, outperforming state-of-the-art models.