Textual entailment is a fundamental task in natural language processing. It refers to the directional relation between text fragments such that the "premise" can infer "hypothesis". In recent years deep learning methods have achieved great success in this task. Many of them have considered the inter-sentence word-word interactions between the premise-hypothesis pairs, however, few of them considered the "asymmetry" of these interactions. Different from paraphrase identification or sentence similarity evaluation, textual entailment is essentially determining a directional (asymmetric) relation between the premise and the hypothesis. In this paper, we propose a simple but effective way to enhance existing textual entailment algorithms by using asymmetric word embeddings. Experimental results on SciTail and SNLI datasets show that the learned asymmetric word embeddings could significantly improve the word-word interaction based textual entailment models. It is noteworthy that the proposed AWE-DeIsTe model can get 2.1% accuracy improvement over prior state-of-the-art on SciTail.