Supervised contrastive learning (SCL) frameworks treat each class as independent and thus consider all classes to be equally important. This neglects the common scenario in which label hierarchy exists, where fine-grained classes under the same category show more similarity than very different ones. This paper introduces a family of Label-Aware SCL methods (LASCL) that incorporates hierarchical information to SCL by leveraging similarities between classes, resulting in creating a more well-structured and discriminative feature space. This is achieved by first adjusting the distance between instances based on measures of the proximity of their classes with the scaled instance-instance-wise contrastive. An additional instance-center-wise contrastive is introduced to move within-class examples closer to their centers, which are represented by a set of learnable label parameters. The learned label parameters can be directly used as a nearest neighbor classifier without further finetuning. In this way, a better feature representation is generated with improvements of intra-cluster compactness and inter-cluster separation. Experiments on three datasets show that the proposed LASCL works well on text classification of distinguishing a single label among multi-labels, outperforming the baseline supervised approaches. Our code is publicly available.