The sequential recommendation, which models sequential behavioral patterns among users for the recommendation, plays a critical role in recommender systems. Conventionally, user general taste and recent demand are combined to promote recommendation performance. However, existing methods usually neglect that user long-term preference keeps evolving over time and only use a static user embedding to model the general taste. Moreover, they often ignore the feature interactions when modeling short-term sequential patterns and integrate user-item or item-item interactions through a linear way, which limits the capability of model. To this end, we propose an Attention and Convolution enhanced memory network for Sequential Recommendation (ACSR) in this paper. Specifically, an attention layer learns user’s general preference, while the convolutional layer searches for feature interactions and sequential patterns to capture user’s sequential preference. Moreover, the outputs of the attention layer and the convolutional layer are concatenated and fed into a fully-connected layer to generate the recommendation. This approach provides a unified and flexible network structure for capturing both general taste and sequential preference. Finally, we evaluate our model on two real-world datasets. Extensive experimental results show that our model ACSR outperforms the state-of-the-art approaches.