To solve the problem in most of conventional multi-task learning algorithms which evaluate risk independently for single task and lack uniform constraint across all tasks, a new hyper-spherical multi-task learning algorithm with adaptive grouping was proposed in this paper. Based on Extreme Learning Machine (ELM) as basic framework, this algorithm introduced hyper-spherical loss function to evaluate the risks of all tasks uniformly, and got decision model via iterative reweighted least squares solution. Furthermore, considering the existence of relatedness between tasks, this paper also constructed regularizer with grouping structure based on the assumption that related tasks had more similar weight vector, which would make the tasks in same group be trained independently. Finally, the optimization object was transformed into a mixed 0-1 programming problem, and a multi-objective method was utilized to identify optimal grouping structure and get model parameters. The simulation results on toy data and cylindrical vibration signal data show that the proposed algorithm outperforms state-of-the-art methods in terms of generalization performance and the ability of identifying inner structure in tasks.