A great challenge in speaker representation learning using deep models is to design learning objectives that can enhance the discrimination of unseen speakers under unseen domains. This work proposes a supervised contrastive learning objective to learn a speaker embedding space by effectively leveraging the label information in the training data. In such a space, utterance pairs spoken by the same or similar speakers will stay close, while utterance pairs spoken by different speakers will be far apart. For each training speaker, we perform random data augmentation on their utterances to form positive pairs, and utterances from different speakers form negative pairs. To maximize speaker separability in the embedding space, we incorporate the additive angular-margin loss into the contrastive learning objective. Experimental results on CN-Celeb show that this new learning objective can cause ECAPA-TDNN to find an embedding space that exhibits great speaker discrimination. The contrastive learning objective is easy to implement, and we provide PyTorch code at https://github.com/shanmon110/AAMSupCon.