Inferencing Gene Regulatory Networks (GRNs) from gene expression data is a pivotal challenge in systems biology, and several innovative computational methods have been introduced. However, most of these studies have not considered the skewed degree distribution of genes. Specifically, some genes may regulate multiple target genes while some genes may be regulated by multiple regulator genes. Such a skewed degree distribution issue significantly complicates the application of directed graph embedding methods. To tackle this issue, we propose the Cross-Attention Complex Dual Graph Embedding Model (XATGRN). Our XATGRN employs a cross-attention mechanism to effectively capture intricate gene interactions from gene expression profiles. Additionally, it uses a Dual Complex Graph Embedding approach to manage the skewed degree distribution, thereby ensuring precise prediction of regulatory relationships and their directionality. Our model consistently outperforms existing state-of-the-art methods across various datasets, underscoring its efficacy in elucidating complex gene regulatory mechanisms. Our codes used in this paper are publicly available at: https://github.com/kikixiong/XATGRN.