User response prediction makes a crucial contribution to the rapid development of online advertising system and recommendation system. The importance of learning feature interactions has been emphasized by many works. Many deep models are proposed to automatically learn high-order feature interactions. Since most features in advertising system and recommendation system are high-dimensional sparse features, deep models usually learn a low-dimensional distributed representation for each feature in the bottom layer. Besides traditional fully-connected architectures, some new operations, such as convolutional operations and product operations, are proposed to learn feature interactions better. In these models, the representation is shared among different operations. However, the best representation for different operations may be different. In this paper, we propose a new neural model named Operation-aware Neural Networks (ONN) which learns different representations for different operations. Our experimental results on two large-scale real-world ad click/conversion datasets demonstrate that ONN consistently outperforms the state-of-the-art models in both offline-training environment and online-training environment.