Unsupervised domain adaptation person re-identification (Re-ID) aims to identify pedestrian images within an unlabeled target domain with an auxiliary labeled source-domain dataset. Many existing works attempt to recover reliable identity information by considering multiple homogeneous networks. And take these generated labels to train the model in the target domain. However, these homogeneous networks identify people in approximate subspaces and equally exchange their knowledge with others or their mean net to improve their ability, inevitably limiting the scope of available knowledge and putting them into the same mistake. This paper proposes a Dual-level Asymmetric Mutual Learning method (DAML) to learn discriminative representations from a broader knowledge scope with diverse embedding spaces. Specifically, two heterogeneous networks mutually learn knowledge from asymmetric subspaces through the pseudo label generation in a hard distillation manner. The knowledge transfer between two networks is based on an asymmetric mutual learning manner. The teacher network learns to identify both the target and source domain while adapting to the target domain distribution based on the knowledge of the student. Meanwhile, the student network is trained on the target dataset and employs the ground-truth label through the knowledge of the teacher. Extensive experiments in Market-1501, CUHK-SYSU, and MSMT17 public datasets verified the superiority of DAML over state-of-the-arts.