The Massive Open Online Course (MOOC) has expanded significantly in recent years. With the widespread of MOOC, the opportunity to study the fascinating courses for free has attracted numerous people of diverse educational backgrounds all over the world. In the big data era, a key research topic for MOOC is how to mine the needed courses in the massive course databases in cloud for each individual student accurately and rapidly as the number of courses is increasing fleetly. In this respect, the key challenge is how to realize personalized course recommendation as well as to reduce the computing and storage costs for the tremendous course data. In this paper, we propose a big data-supported, context-aware online learning-based course recommender system that could handle the dynamic and infinitely massive datasets, which recommends courses by using personalized context information and historical statistics. The context-awareness takes the personal preferences into consideration, making the recommendation suitable for people with different backgrounds. Besides, the algorithm achieves the sublinear regret performance, which means it can gradually recommend the mostly preferred and matched courses to students. In addition, our storage module is expanded to the distributed-connected storage nodes, where the devised algorithm can handle massive course storage problems from heterogeneous sources of course datasets. Comparing to existing algorithms, our proposed algorithms achieve the linear time complexity and space complexity. Experiment results verify the superiority of our algorithms when comparing with existing ones in the MOOC big data setting.