Matrix factorization has been a key technique in learning latent factor models for many applications in computer vision and pattern recognition such as image annotation and collaborative prediction. Specifically, in collaborative filtering problems, the goal of matrix factorization is to predict the missing values based on the low-rank factorization gained based on observed entries. Among various algorithms, maximum margin matrix factorization has been a successful approach to discriminative collaborative filtering problems, where the input matrix is binary. In this paper, we consider the problem of one-class discriminative collaborative filtering, where the data matrix is binary and only positive values can be observed, i.e. the entries of data matrix can be either observed as positive or missing. Many real applications fall in this category. For example, given an image with incomplete tag list: cat, tree, garden, we are only sure the image has cat while not sure whether it has grass or not since the tag list is incomplete. To cope with this problem, one-class Maximum Margin Matrix Factorization (one-class MMMF), which inherits the merits of both the applicability of one-class SVM and the discriminative power of maximum margin matrix factorization, is proposed. Extensive experiments conducted on both simulated toy data and real benchmark image datasets demonstrate that the proposed approach is considerably superior to the traditional approaches, which simply assume unobserved entries as negative.