To solve the large-scale online learning problem, this paper proposes a bidimensionally partitioned sequential regularized extreme learning machine(BP-SRELM). Based on the online sequential extreme learning machine, combining the divide-and-conquer strategy, the BP-SRELM partitions a high-dimensional hidden layer output matrix into several small matrices from the aspects of instance dimension and feature dimension, so as to reduce the scale and the complexity of the problem, and consequently, the execution efficiency of the algorithm for large-scale learning problem is significantly improved. Meanwhile, the Tikhonov regularization technology is incorporated in the BP-SRELM to further enhance the stability and the generalization capability of the algorithm in real applications. Experimental results show that the proposed BP-SRELM can provide better performances in the sense of stability and prediction accuracy with greatly improved leaning speed than its counterparts, and it can be applied to the online learning and real-time modeling of large-scale data streams.