Human-Object Interaction (HOI) detection plays a vital role in scene understanding, which aims to predict the HOI triplet in the form of <human, object, action>. Existing methods mainly extract multi-modal features (e.g., appearance, object semantics, human pose) and then fuse them together to directly predict HOI triplets. However, most of these methods focus on seeking for self-triplet aggregation, but ignore the potential cross-triplet dependencies, resulting in ambiguity of action prediction. In this work, we propose to explore Self- and Cross-Triplet Correlations (SCTC) for HOI detection. Specifically, we regard each triplet proposal as a graph where Human, Object represent nodes and Action indicates edge, to aggregate self-triplet correlation. Also, we try to explore cross-triplet dependencies by jointly considering instance-level, semantic-level, and layout-level relations. Besides, we leverage the CLIP model to assist our SCTC obtain interaction-aware feature by knowledge distillation, which provides useful action clues for HOI detection. Extensive experiments on HICO-DET and V-COCO datasets verify the effectiveness of our proposed SCTC.