Wafer classification is a critical task for semiconductor manufacturing. Most conventional algorithms require a large-scale perfectly labeled dataset to train accurate classifiers. In practice, it is usually difficult or even impossible to collect perfect labels without errors, and the classification accuracy in the presence of imperfectly labeled data would degrade. To facilitate robust wafer classification with noisy labels, we propose a novel self-boosting co-teaching (SB-CT) approach. Specifically, we iteratively correct the wrong labels by using the predictions of two classifiers that are jointly trained with noisily labeled data. To make the proposed method of practical utility, we develop a novel method to accurately estimate the noise rate, and adopt a probability scaling technique to further improve the classification accuracy. As demonstrated by the experimental results based on two industrial datasets, the proposed SB-CT approach achieves superior accuracy over other conventional methods.