Pre-trained models have brought remarkable success on the text summarization task. For dialogue summarization, the subdomain of text summarization, utterances are concatenated to flat text before being processed. As a result, existing summarization systems based on pre-trained models are unable to recognize the unique format of the speaker-utterance pair well in the dialogue. To investigate this issue, we conduct probing tests and manual analysis, and find that the powerful pre-trained model can not identify different speakers well in the conversation, which leads to various factual errors. Moreover, we propose three speaker-aware supervised contrastive learning (SCL) tasks: Token-level SCL, Turn-level SCL, and Global-level SCL. Comprehensive experiments demonstrate that our methods achieve significant performance improvement on two mainstream dialogue summarization datasets. According to detailed human evaluations, pre-trained models equipped with SCL tasks effectively generate summaries with better factual consistency.