As an interesting and challenging task, story ending generation aims at generating a reasonable and coherent ending for a given story context. The key challenge of the task is to comprehend the context sufficiently and capture the hidden logic information effectively, which has not been well explored by most existing generative models. To tackle this issue, we propose a context-aware Multi-level Graph Convolutional Networks over Dependency Parse (MGCN-DP) trees to capture dependency relations and context clues more effectively. We utilize dependency parse trees to facilitate capturing relations and events in the context implicitly, and Multi-level Graph Convolutional Networks to update and deliver the representation crossing levels to obtain richer contextual information. Both automatic and manual evaluations show that our MGCN-DP can achieve comparable performance with state-of-the-art models. Our source code is available at https://github.com/VISLANG-Lab/MLGCN-DP.