Aspect term extraction aims to extract aspect terms from a review sentence that users have expressed opinions on. One of the remaining challenges for aspect term extraction resides in the lack of sufficient annotated data. While self-training is potentially an effective method to address this issue, the pseudo-labels it yields on unlabeled data could induce noise. In this paper, we use two means to alleviate the noise in the pseudo-labels. One is that inspired by the curriculum learning, we refine the conventional self-training to progressive self-training. Specifically, the base model infers pseudo-labels on a progressive subset at each iteration, where samples in the subset become harder and more numerous as the iteration proceeds. The other is that we use a discriminator to filter the noisy pseudo-labels. Experimental results on four SemEval datasets show that our model significantly outperforms the previous baselines and achieves state-of-the-art performance.