A proper representation that can well express the characteristics of a word plays an important role in wake-up word detection (WWD). However, it may be easily corrupted due to various types of environmental noise occurred in the place where WWD typically works, causing unreliable performance. To deal with this practical issue, we propose a novel strategy called cross-informed domain adversarial training (CiDAT) for noise-robust WWD. In the method, additional paths were introduced to conventional domain adversarial training (DAT) to encourage its ability to generate domain-invariant representation. Experiments on the Aurora4 corpus verified that CiDAT significantly outperformed the baselines as well as conventional DAT.