In this work, we contribute a new multi-layer neural network architecture named ONCF to perform collaborative filtering. The idea is to use an outer product to explicitly model the pairwise correlations between the dimensions of the embedding space. In contrast to existing neural recommender models that combine user embedding and item embedding via a simple concatenation or element-wise product, our proposal of using outer product above the embedding layer results in a two-dimensional interaction map that is more expressive and semantically plausible. Above the interaction map obtained by outer product, we propose to employ a convolutional neural network to learn high-order correlations among embedding dimensions. Extensive experiments on two public implicit feedback data demonstrate the effectiveness of our proposed ONCF framework, in particular, the positive effect of using outer product to model the correlations between embedding dimensions in the low level of multi-layer neural recommender model.