From an engineering perspective, a design should not only perform well in an ideal condition, but should also resist noises. Such a design methodology, namely robust design, has been widely implemented in the industry for product quality control. However, classic robust design requires a lot of evaluations for a single design target, while the results of these evaluations could not be reused for a new target. To achieve a data-efficient robust design, we propose Robust Inverse Design under Noise (RID-Noise), which can utilize existing noisy data to train a conditional invertible neural network (cINN). Specifically, we estimate the robustness of a design parameter by its predictability, measured by the prediction error of a forward neural network. We also define a sample-wise weight, which can be used in the maximum weighted likelihood estimation of an inverse model based on a cINN. With the visual results from experiments, we clearly justify how RID-Noise works by learning the distribution and robustness from data. Further experiments on several real-world benchmark tasks with noises confirm that our method is more effective than other state-of-the-art inverse design methods. Code and supplementary is publicly available at https://github.com/ThyrixYang/rid-noise-aaai22