One-shot automated essay scoring (AES) aims to assign scores to a set of essays written specific to a certain prompt, with only one manually scored essay per distinct score. Compared to the previous-studied prompt-specific AES which usually requires a large number of manually scored essays for model training (e.g., about 600 manually scored essays out of totally 1000 essays), one-shot AES can greatly reduce the workload of manual scoring. In this paper, we propose a Transductive Graph-based Ordinal Distillation (TGOD) framework to tackle the task of one-shot AES. Specifically, we design a transductive graph-based model as a teacher model to generate pseudo labels of unlabeled essays based on the one-shot labeled essays. Then, we distill the knowledge in the teacher model into a neural student model by learning from the high confidence pseudo labels. Different from the general knowledge distillation, we propose an ordinal-aware unimodal distillation which makes a unimodal distribution constraint on the output of student model, to tolerate the minor errors existed in pseudo labels. Experimental results on the public dataset ASAP show that TGOD can improve the performance of existing neural AES models under the one-shot AES setting and achieve an acceptable average QWK of 0.69.