Person re-identification aims to match a person's identity across multiple camera streams. Deep neural networks have been successfully applied to the challenging person re-identification task. One remarkable bottleneck is that the existing deep models are data hungry and require large amounts of labeled training data. Acquiring manual annotations for pedestrian identity matchings in large-scale surveillance camera installations is a highly cumbersome task. Here, we propose the first semi-supervised approach that performs pseudo-labeling by considering complex relationships between unlabeled and labeled training samples in the feature space. Our approach first approximates the actual data manifold by learning a generative model via adversarial training. Given the trained model, data augmentation can be performed by generating new synthetic data samples which are unlabeled. An open research problem is how to effectively use this additional data for improved feature learning. To this end, this work proposes a novel Feature Affinity based Pseudo-Labeling (FAPL) approach with two possible label encodings under a unified setting. Our approach measures the affinity of unlabeled samples with the underlying clusters of labeled data samples using the intermediate feature representations from deep networks. FAPL trains with the joint supervision of cross-entropy loss together with a center regularization term, which not only ensures discriminative feature representation learning but also simultaneously predicts pseudo-labels for unlabeled data. Our extensive experiments on two standard large-scale datasets, Market-1501 and DukeMTMC-reID, demonstrate significant performance boosts over closely related competitors and outperforms state-of-the-art person re-identification techniques in most cases.