Graphs are ubiquitous in many applications, such as social networks, knowledge graphs, smart grids, etc.. Graph neural networks (GNN) are the current state-of-the-art for these applications, and yet remain obscure to humans. Explaining the GNN predictions can add transparency. However, as many graphs are not static but continuously evolving, explaining changes in predictions between two graph snapshots is different but equally important. Prior methods only explain static predictions or generate coarse or irrelevant explanations for dynamic predictions. We define the problem of explaining evolving GNN predictions and propose an axiomatic attribution method to uniquely decompose the change in a prediction to paths on computation graphs. The attribution to many paths involving high-degree nodes is still not interpretable, while simply selecting the top important paths can be suboptimal in approximating the change. We formulate a novel convex optimization problem to optimally select the paths that explain the prediction evolution. Theoretically, we prove that the existing method based on Layer-Relevance-Propagation (LRP) is a special case of the proposed algorithm when an empty graph is compared with. Empirically, on seven graph datasets, with a novel metric designed for evaluating explanations of prediction change, we demonstrate the superiority of the proposed approach over existing methods, including LRP, DeepLIFT, and other path selection methods.