Domain adaptation solves image classification problems in the target domain by taking advantage of the labelled source data and unlabelled target data. Usually, the source and target domains share the same set of classes. As a special case, Open-Set Domain Adaptation (OSDA) assumes there exist additional classes in the target domain but not present in the source domain. To solve such a domain adaptation problem, our proposed method learns discriminative common subspaces for the source and target domains using a novel Open-Set Locality Preserving Projection (OSLPP) algorithm. The source and target domain data are aligned in the learned common spaces class-wisely. To handle the open-set classification problem, our method progressively selects target samples to be pseudo-labelled as known classes and rejects the outliers if they are detected as from unknown classes. The common subspace learning algorithm OSLPP simultaneously aligns the labelled source data and pseudo-labelled target data from known classes and pushes the rejected target data away from the known classes. The common subspace learning and the pseudo-labelled sample selection/rejection facilitate each other in an iterative learning framework and achieves state-of-the-art performance on benchmark datasets Office-31 and Office-Home with the average HOS of 87.4% and 67.0% respectively.