The performance of person re-identification (Re-ID) has been seriously effected by the large cross-view appearance variations caused by mutual occlusions and background clutters. Hence learning a feature representation that can adaptively emphasize the foreground persons becomes very critical to solve the person Re-ID problem. In this paper, we propose a simple yet effective foreground attentive neural network (FANN) to learn a discriminative feature representation for person Re-ID, which can adaptively enhance the positive side of foreground and weaken the negative side of background. Specifically, a novel foreground attentive subnetwork is designed to drive the networks attention, in which a decoder network is used to reconstruct the binary mask by using a novel local regression loss function, and an encoder network is regularized by the decoder network to focus its attention on the foreground persons. The resulting feature maps of encoder network are further fed into the body part subnetwork and feature fusion subnetwork to learn discriminative features. Besides, a novel symmetric triplet loss function is introduced to supervise feature learning, in which the intra-class distance is minimized and the inter-class distance is maximized in each triplet unit, simultaneously. Training our FANN in a multi-task learning framework, a discriminative feature representation can be learned to find out the matched reference to each probe among various candidates in the gallery. Extensive experimental results on several public benchmark datasets are evaluated, which have shown clear improvements of our method over the state-of-the-art approaches.