Aspect sentiment classification, a challenging task in sentiment analysis, has been attracting more and more attention in recent years. In this paper, we highlight the need for incorporating the importance degrees of both words and clauses inside a sentence and propose a hierarchical network with both word-level and clause-level attentions to aspect sentiment classification. Specifically, we first adopt sentence-level discourse segmentation to segment a sentence into several clauses. Then, we leverage multiple Bi-directional LSTM layers to encode all clauses and propose a word-level attention layer to capture the importance degrees of words in each clause. Third and finally, we leverage another Bi-directional LSTM layer to encode the outputs from the former layers and propose a clause-level attention layer to capture the importance degrees of all the clauses inside a sentence. Experimental results on the laptop and restaurant datasets from SemEval-2015 demonstrate the effectiveness of our proposed approach to aspect sentiment classification.