Most person re-identification (ReID) approaches assume that person images are captured under relatively similar illumination conditions. In reality, long-term person retrieval is common, and person images are often captured under different illumination conditions at different times across a day. In this situation, the performances of existing ReID models often degrade dramatically. This paper addresses the ReID problem with illumination variations and names it as {\em Illumination-Adaptive Person Re-identification (IA-ReID)}. We propose an Illumination-Identity Disentanglement (IID) network to dispel different scales of illuminations away while preserving individuals' identity information. To demonstrate the illumination issue and to evaluate our model, we construct two large-scale simulated datasets with a wide range of illumination variations. Experimental results on the simulated datasets and real-world images demonstrate the effectiveness of the proposed framework.