Triplet loss has been proposed to increase the inter-class distance and decrease the intra-class distance for various tasks of image recognition. However, for facial expression recognition (FER) problem, the fixed margin parameter does not fit the diversity of scales between different expressions. Meanwhile, the strategy of selecting the hardest triplets can introduce noisy guidance information since various persons may present significantly different expressions. In this work, we propose a new triplet loss based on class-aware margins and outlier-suppressed triplet for FER, where each pair of expressions, e.g. 'happy' and 'fear', is assigned with an adaptive margin parameter and the abnormal hard triplets are discarded according to the feature distance distribution. Experimental results of the proposed triplet loss on the FER2013 and CK+ expression databases show that the proposed network achieves much better accuracy than the original triplet loss and the network without using the proposed strategies, and competitive performance compared with the state-of-the-art algorithms.