Inspired by the significant success of deep learning, some attempts have been made to introduce deep neural networks (DNNs) in recommendation systems to learn users' preferences for items. Since DNNs are well suitable for representation learning, they enable recommendation systems to generate more accurate prediction. However, they inevitably result in high computational and storage costs. Worse still, due to the relatively small number of ratings that can be fed into DNNs, they may easily lead to over-fitting. To tackle these problems, we propose a novel recommendation algorithm based on Back Propagation (BP) neural network with Attention Mechanism (BPAM). In particular, the BP neural network is utilized to learn the complex relationship of the target users and their neighbors. Compared with deep neural network, the shallow neural network, i.e., BP neural network, can not only reduce the computational and storage costs, but also prevent the model from over-fitting. In addition, an attention mechanism is designed to capture the global impact on all nearest target users for each user.  Extensive experiments on eight benchmark datasets have been conducted to evaluate the effectiveness of the proposed model.