In real world person re-identification (re-id), images of people captured at very different resolutions from different locations need be matched. Existing re-id models typically normalise all person images to the same size. However, a low-resolution (LR) image contains much less information about a person, and direct image scaling and simple size normalisation as done in conventional re-id methods cannot compensate for the loss of information. To solve this LR person re-id problem, we propose a novel joint multi-scale learning framework, termed joint multi-scale discriminant component analysis (JUDEA). The key component of this framework is a heterogeneous class mean discrepancy (HCMD) criterion for cross-scale image domain alignment, which is optimised simultaneously with discriminant modelling across multiple scales in the joint learning framework. Our experiments show that the proposed JUDEA framework outperforms existing representative reid methods as well as other related LR visual matching models applied for the LR person re-id problem.