Recently, contrastive learning has shown great potential in medical image segmentation. Due to the lack of expert annotations, however, it is challenging to apply contrastive learning in semi-supervised scenes. To solve this problem, we propose a novel uncertainty-guided pixel contrastive learning method for semi-supervised medical image segmentation. Specifically, we construct an uncertainty map for each unlabeled image and then remove the uncertainty region in the uncertainty map to reduce the possibility of noise sampling. The uncertainty map is determined by a well-designed consistency learning mechanism, which generates comprehensive predictions for unlabeled data by encouraging consistent network outputs from two different decoders. In addition, we suggest that the effective global representations learned by an image encoder should be equivariant to different geometric transformations. To this end, we construct an equivariant contrastive loss to strengthen global representation learning ability of the encoder. Extensive experiments conducted on popular medical image benchmarks demonstrate that the proposed method achieves better segmentation performance than the state-of-the-art methods.