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Video Object Grounding (VOG) is the problem of associating spatial object regions in the video to a descriptive natural language query. This is a challenging vision-language task that necessitates constructing the correct cross-modal correspondence and modeling the appropriate spatio-temporal context of the query video and caption, thereby localizing the specific objects accurately. In this paper, we tackle this task by a novel framework called HiErarchical spatio-tempoRal reasOning (HERO) with contrastive action correspondence. We study the VOG task at two aspects that prior works overlooked: (1) Contrastive Action Correspondence-aware Retrieval. Notice that the fine-grained video semantics (e.g., multiple actions) is not totally aligned with the annotated language query (e.g., single action), we first introduce the weakly-supervised contrastive learning that classifies the video as action-consistent and action-independent frames relying on the video-caption action semantic correspondence. Such a design can build the fine-grained cross-modal correspondence for more accurate subsequent VOG. (2) Hierarchical Spatio-temporal Modeling Improvement. While transformer-based VOG models present their potential in sequential modality (i.e., video and caption) modeling, existing evidence also indicates that the transformer suffers from the issue of the insensitive spatio-temporal locality. Motivated by that, we carefully design the hierarchical reasoning layers to decouple fully connected multi-head attention and remove the redundant interfering correlations. Furthermore, our proposed pyramid and shifted alignment mechanisms are effective to improve the cross-modal information utilization of neighborhood spatial regions and temporal frames. We conducted extensive experiments to show our HERO outperforms existing techniques by achieving significant improvement on two benchmark datasets.