Chromatin interactions play critical roles in gene regulation. The genomes of distinct maize inbreds exhibit substantial structural variation, however, F1 hybrids lead to significant hybrid vigor. The long-range genomic interactions present in different inbreds and their hybrid offspring have not been assessed in maize. Here, we perform H3K4me3/H3K27ac HiChIP in two maize inbreds and their reciprocal F1 hybrids. We identify interactions specific to inbred or hybrid genotypes. Some genes involved in hybrid-specific interactions show dominant or over-dominant expression patterns. The analysis of the inbred-specific or shared interactions between two parental inbred lines in the hybrids reveal unexpected gain or loss of interactions compared to the parents. The unexpected hybrid interactions are partially associated with unexpected gene regulation patterns. We also identify some inter-allelic interactions in hybrids, suggesting potential somatic chromosome interactions in maize. Our analyses of 3D regulatory networks provide a potential explanation for non-additive gene expression in maize hybrids.