In massive multiple-input multiple-output (MIMO) system, Neumann series (NS) expansion-based linear minimum mean square error (LMMSE) detection has been proposed due to its simple and efficient multi-stage pipeline hardware implementation. However, it suffers from poor performance and slow convergence as the number of the users grows. To address this issue, we proposed a novel weighted Neumann series (WNS)-based LMMSE detection to minimize the error between the exact matrix inversion and the WNS-based matrix inversion. Moreover, the optimal weights are obtained according to on-line learning basis. Numerical results indicate that the learning-based WNS detection outperforms the conventional NS-based detection and achieves near-LMMSE performance with a significantly lower computational complexity.