Compositional image retrieval (CIR) is a challenging retrieval task, where the query is composed of a reference image and a modification text, and the target is another image reflecting the modification to the reference image. Due to the great success of the pre-trained vision-and-language model CLIP and its favorable applicability to large-scale retrieval tasks, we propose a CIR model HyCoLe-HNM with CLIP as the backbone. In HyCoLe-HNM, we follow the contrastive pre-training method of CLIP to perform cross-modal representation learning. On this basis, we propose a hybrid compositional learning mechanism, which includes both image compositional learning and text compositional learning. In hybrid compositional learning, we borrow a gated fusion mechanism from a question answering model to perform compositional fusion, and propose a heuristic negative mining method to filter negative samples. Privileged information in the form of image-related texts is utilized in cross-modal representation learning and hybrid compositional learning. Experimental results show that HyCoLe-HNM achieves state-of-the-art performance on three CIR datasets, namely FashionIQ, Fashion200K, and MIT-States.