The assessment of children’s narrative ability is crucial for diagnosing language disorders and planning interventions. Distinct from the typical automated essay scoring, this task focuses primarily on evaluating the completeness of narrative content and the coherence of expression, as well as the interpretability of assessment results. To address these issues, we propose a novel computational assessing framework NarGINA, under which the narrative graph is introduced to provide a concise and structured summary representation of narrative text, allowing for explicit narrative measurement. To this end, we construct the first Chinese children’s narrative assessment corpus based on real children’s narrative samples, and we then design a narrative graph construction model and a narrative graph-assisted scoring model to yield accurate narrative ability assessment. Particularly, to enable the scoring model to understand narrative graphs, we propose a multi-view graph contrastive learning strategy to pre-train the graph encoder and apply instruction-tuned large language models to generate scores. The extensive experimental results show that NarGINA can achieve significant performance improvement over the baselines, simultaneously possessing good interpretability. Our findings reveal that the utilization of structured narrative graphs beyond flat text is well suited for narrative ability assessment. The model and data are publicly available at https://github.com/JlexZzz/NarGINA.