Compositional zero-shot learning (CZSL) aims to identify unobservable compositional concepts with prior knowledge of known primitives (attributes and objects). Due to distribution differences between seen and unseen components, existing methods for CZSL often ignore intrinsic variations between primitives and suffer from domain bias problems. To address this challenge, we proposed a concept-aware graph convolutional network (GCN) that utilizes cross-attentions to extract features unique to attributes and objects from paired concept-sharing inputs. The proposed model utilizes the cosine similarity between visual features and synthetic embeddings to estimate the feasibility score for each unseen composition. This score is then employed as a weight in the graph adjacency matrix. Additionally, the proposed model incorporates the Earth mover's distance (EMD) to further limit the concept of learning interest in disentanglers. Experimental results on three challenging dataset benchmarks, including UT-Zappos 50K, C-GQA, and MIT-States, demonstrate that the proposed model outperforms prior work in both closed- and open-world CZSL (OW-CZSL).