Space-division multiplexing (SDM) has been expected to support the continuous growth of transmission capacity. However, it suffers from high computation complexity that limits its physical implementations. In this paper, we propose and experimentally demonstrate a low-complexity MIMO equalization method to leverage the sparsity of weights and reduce the complexity by L1&L2-regularization in long-haul space-division multiplexing (SDM) systems. The L1-regularization finds the sparse solution of equalizer filters and substitutes it for optimal solution, reducing the complexity with performance degradation. On the other hand, the L2-regularization tends to produce a smoother estimation than L1 regularization and is therefore more robust to large variance. We conduct a 39.87-GBaud QPSK coherent optical transmission experiment based on a 4-core coupled-core fiber with the transmission distance from 1206-km to 7236-km. Comparisons on the equalization performance and computational complexity show that the sparse equalizer using L1&L2-regularization achieves a 30% reduction in complexity at the similar system performance, compared with the traditional time-domain MIMO.