Multi-Task Learning (MTL) can enhance the classifier's generalization performance by learning multiple related tasks simultaneously. Conventional MTL works under the offline or batch learning setting and suffers from the expensive training cost together with the poor scalability. To address such inefficiency issues, online learning technique has been applied to solve MTL problems. However, most existing algorithms for online MTL constrain task relatedness into a presumed structure via a single weight matrix, a strict restriction that does not always hold in practice. In this paper, we propose a general online MTL framework that overcomes this restriction by decomposing the weight matrix into two components: the first component captures the correlative structure among tasks in a low-rank subspace, and the second component identifies the personalized patterns for the outlier tasks. A projected gradient scheme is devised to learn such components adaptively. Theoretical analysis shows that the proposed algorithm can achieve a sub-linear regret with respect to the best linear model in hindsight. Experimental investigation on a number of real-world datasets also verifies the efficacy of our approach.