Sequential recommendation predicts users' next behaviors with their historical interactions. Recommending with longer sequences improves recommendation accuracy and increases the degree of personalization. As sequences get longer, existing works have not yet addressed the following two main challenges. Firstly, modeling long-range intra-sequence dependency is difficult with increasing sequence lengths. Secondly, it requires efficient memory and computational speeds. In this paper, we propose a Sparse Attentive Memory (SAM) network for long sequential user behavior modeling. SAM supports efficient training and real-time inference for user behavior sequences with lengths on the scale of thousands. In SAM, we model the target item as the query and the long sequence as the knowledge database, where the former continuously elicits relevant information from the latter. SAM simultaneously models target-sequence dependencies and long-range intra-sequence dependencies with O(L) complexity and O(1) number of sequential updates, which can only be achieved by the self-attention mechanism with O(L^2) complexity. Extensive empirical results demonstrate that our proposed solution is effective not only in long user behavior modeling but also on short sequences modeling. Implemented on sequences of length 1000, SAM is successfully deployed on one of the largest international E-commerce platforms. This inference time is within 30ms, with a substantial 7.30% click-through rate improvement for the online A/B test. To the best of our knowledge, it is the first end-to-end long user sequence modeling framework that models intra-sequence and target-sequence dependencies with the aforementioned degree of efficiency and successfully deployed on a large-scale real-time industrial recommender system.