Conversational emotion recognition (CER) has attracted increasing interests in the natural language processing (NLP) community. Different from the vanilla emotion recognition, effective speaker-sensitive utterance representation is one major challenge for CER. In this paper, we exploit speaker identification (SI) as an auxiliary task to enhance the utterance representation in conversations. By this method, we can learn better speaker-aware contextual representations from the additional SI corpus. Experiments on two benchmark datasets demonstrate that the proposed architecture is highly effective for CER, obtaining new state-of-the-art results on two datasets.