Traditional recommendation models grapple with challenges such as the scarcity of similar user or item references and data sparsity, rendering the cold-start problem particularly formidable. Meta-learning has emerged as a promising avenue to address these issues, particularly in solving the item cold-start problem by generating meta-embeddings for new items as their initial ID embeddings. This approach has shown notable success in enhancing the accuracy of click-through rate predictions. However, prevalent meta-embedding models often focus solely on the attribute features of the item, neglecting crucial user information associated with it during the generation of initial ID embeddings for new items. This oversight hinders the exploitation of valuable user-related information to enhance the quality and accuracy of the initial ID embedding. To tackle this limitation, we introduce the residual graph meta-embedding model (RGMeta). RGMeta adopts a comprehensive approach by considering both the attribute features and target users of both old and new items. Through the integration of residual connections, the model effectively combines the representation information of the old neighbor items with the intrinsic features of the new item, resulting in an improved initial ID embedding generation. Experimental results demonstrate that RGMeta significantly enhances the performance of the cold-start phase, showcasing its effectiveness in overcoming challenges associated with sparse data and limited reference points. Our proposed model presents a promising step forward in leveraging both item attributes and user-related information to address cold-start problems in recommendation systems.