MGMT promoter methylation and IDH1 mutation in high-grade gliomas (HGG) have proven to be the two important molecular indicators associated with better prognosis. Traditionally, the statuses of MGMT and IDH1 are obtained via surgical biopsy, which is laborious, invasive and time-consuming. Accurate presurgical prediction of their statuses based on preoperative imaging data is of great clinical value towards better treatment plan. In this paper, we propose a novel Multi-label Inductive Matrix Completion (MIMC) model, highlighted by the online inductive learning strategy, to jointly predict both MGMT and IDH1 statuses. Our MIMC model not only uses the training subjects with possibly missing MGMT/IDH1 labels, but also leverages the unlabeled testing subjects as a supplement to the limited training dataset. More importantly, we learn inductive labels, instead of directly using transductive labels, as the prediction results for the testing subjects, to alleviate the overfitting issue in small-sample-size studies. Furthermore, we design an optimization algorithm with guaranteed convergence based on the block coordinate descent method to solve the multivariate non-smooth MIMC model. Finally, by using a precious single-center multi-modality presurgical brain imaging and genetic dataset of primary HGG, we demonstrate that our method can produce accurate prediction results, outperforming the previous widely-used single- or multi-task machine learning methods. This study shows the promise of utilizing imaging-derived brain connectome phenotypes for prognosis of HGG in a non-invasive manner.