Multimedia recommendation aims to fuse the multi-modal information of items for feature enrichment to improve the recommendation performance. However, existing methods typically introduce multi-modal information based on collaborative information to improve the overall recommendation precision, while failing to explore its cold-start recommendation performance. Meanwhile, these above methods are only applicable when such multi-modal data is available. To address this problem, this paper proposes a recommendation framework, named Cross-modal Content Inference and Feature Enrichment Recommendation (CIERec), which exploits the multi-modal information to improve its cold-start recommendation performance. Specifically, CIERec first introduces image annotation as the privileged information to help guide the mapping of unified features from the visual space to the semantic space in the training phase. And then CIERec enriches the content representation with the fusion of collaborative, visual, and cross-modal inferred representations, so as to improve its cold-start recommendation performance. Experimental results on two real-world datasets show that the content representations learned by CIERec are able to achieve superior cold-start recommendation performance over existing visually-aware recommendation algorithms. More importantly, CIERec can consistently achieve significant improvements with different conventional visually-aware backbones, which verifies its universality and effectiveness.