Contrastive learning is a powerful paradigm for representation learning with prominent success in computer vision and NLP, but how to extend its success to high-dimensional tensors remains a challenge. This is because tensor data often exhibit high-order mode-interactions that are hard to profile and with negative samples growing combinatorially faster than second-order contrastive learning; furthermore, many real-world tensors have ordinal entries that necessitate more delicate comparative levels. To solve the challenge, we propose High-Order Contrastive Tensor Completion (HOCTC), an innovative network to extend contrastive learning to sparse ordinal tensor data. HOCTC employs a novel attention-based strategy with query-expansion to capture high-order mode interactions even in case of very limited tokens, which transcends beyond second-order learning scenarios. Besides, it extends two-level comparisons (positive-vs-negative) to fine-grained contrast-levels using ordinal tensor entries as a natural guidance. Efficient sampling scheme is proposed to enforce such delicate comparative structures, generating comprehensive self-supervised signals for high-order representation learning. Extensive experiments show that HOCTC has promising results in sparse tensor completion in traffic/recommender applications.