Semi-supervised learning (SSL), which aims at leveraging a few labeled images and a large number of unlabeled images for network training, is beneficial for relieving the burden of data annotation in medical image segmentation. According to the experience of medical imaging experts, local attributes such as texture, luster and smoothness are very important factors for identifying target objects like lesions and polyps in medical images. Motivated by this, we propose a cross-level contrastive learning scheme to enhance representation capacity for local features in semi-supervised medical image segmentation. Compared to existing image-wise, patch-wise and point-wise contrastive learning algorithms, our devised method is capable of exploring more complex similarity cues, namely the relational characteristics between global and local patch-wise representations. Additionally, for fully making use of cross-level semantic relations, we devise a novel consistency constraint that compares the predictions of patches against those of the full image. With the help of the cross-level contrastive learning and consistency constraint, the unlabelled data can be effectively explored to improve segmentation performance on two medical image datasets for polyp and skin lesion segmentation respectively. Code of our approach is available here.