As the core of recommender system, collaborative filtering (CF) models the affinity between a user and an item from historical user-item interactions, such as clicks, purchases, and so on. Benefited from the strong representation power, neural networks have recently revolutionized the recommendation research, setting up a new standard for CF. However, existing neural recommender models do not explicitly consider the correlations among embedding dimensions, making them less effective in modeling the interaction function between users and items. In this work, we emphasize on modeling the correlations among embedding dimensions in neural networks to pursue higher effectiveness for CF. We propose a novel and general neural collaborative filtering framework, namely ConvNCF, which is featured with two designs: 1) applying outer product on user embedding and item embedding to explicitly model the pairwise correlations between embedding dimensions, and 2) employing convolutional neural network above the outer product to learn the high-order correlations among embedding dimensions. To justify our proposal, we present three instantiations of ConvNCF by using different inputs to represent a user and conduct experiments on two real-world datasets. Extensive results verify the utility of modeling embedding dimension correlations with ConvNCF, which outperforms several competitive CF methods.