Signal detection is a major challenge in massive multiple‐input multiple‐output (MIMO) wireless systems due to array of hundreds of antennas. Linear minimum mean square error (MMSE) enables near‐optimal detection performance in massive MIMO but suffers from unbearable computational complexity due to complicated matrix inversions. To address this problem, we propose a novel low‐complexity signal detector based on joint steepest descent (SD) and non‐stationary Richardson (NSR) iteration method. The SD is applied to get an efficient searching direction for the following NSR method to enhance the performance. The key idea of the proposed algorithm is to utilize a combination of the scaled‐diagonal initialization and the system‐ and iteration‐dependent acceleration mechanism, so that the convergence can be significantly speeded up. An antenna‐ and eigenvalue‐based scaling parameter is introduced for the proposed detector to further improve the error‐rate performance. We also provide convergence guarantees for the proposed technique. Numerical results demonstrate that the proposed joint detection approach attains superior performance compared to existing iterative approaches and provides a lower computational complexity than the conventional MMSE detector.