Study of functional brain network (FBN) based on functional magnetic resonance imaging (fMRI) has proved successful in depression disorder classification. One popular approach to construct FBN is Pearson correlation. However, it only captures pairwise relationship between brain regions, while it ignores the influence of other brain regions. Another common issue existing in many depression disorder classification methods is applying only single local feature extracted from constructed FBN. To address these issues, we develop a new method to classify fMRI data of patients with depression and healthy controls. First, we construct the FBN using a sparse low-rank model, which considers the relationship between two brain regions given all the other brain regions. Moreover, it can automatically remove weak relationship and retain the modular structure of FBN. Secondly, FBN are effectively measured by eight graph-based features from different aspects. Tested on fMRI data of 31 patients with depression and 29 healthy controls, our method achieves 95% accuracy, 96.77% sensitivity, and 93.10% specificity, which outperforms the Pearson correlation FBN and sparse FBN. In addition, the combination of graph-based features in our method further improves classification performance. Moreover, we explore the discriminative brain regions that contribute to depression disorder classification, which can help understand the pathogenesis of depression disorder.