Collaborative filtering is the one of the most successful methods used by recommendation system to solve the information overload problem. Nevertheless, most collaborative filtering only uses explicit rating information to model the user, ignoring the impact of implicit information. In addition, they still utilize inner product to fit user-item interaction behavior, which leads to poor recommendation results. Thus, in this paper, we propose an autoencoder model based on implicit trust relationship between users, where we combine the intrinsic relationship of both the implicit trust information and user-item interaction behavior for collaborative recommendation. Two key challenges emerged in this process: first, how to extract implicit trust information of users, and second, how to model the complex user-item interaction behavior for recommendation. To solve these two challenges, we design a model named the Neural Collaborative Autoencoder for Recommendation with Co-occurrence Embedding (NCAR), which is divided into two parts: (1) the user co-occurrence matrix embedding part; (2) the collaborative neural recommendation part. First, NCAR extracts the user co-occurrence matrix from the rating information. Then, the auto-encoder is used to learn the co-occurrence embedding of each user with the correlation regularization method. Finally, this paper employs an interaction prediction module based on a deep neural network to learn the complex interaction behaviors between users and items. Experiments conducted on four public datasets show that the performance of NCAR is significantly better than that of the baseline method.