In this paper, after showing MMSE-SIC suffers from performance loss when the channel is spatially correlated for Massive MIMO, we propose an effective hybrid iterative detection algorithm named partial Gaussian approach with integer programming (PGA-IP) to handle correlated channels. In PGA-IP, a partial gaussian approach is first employed to reduce the massive MIMO detection (with large dimension Nt ×Nr MIMO channel) to a problem of marginalizing M (M is a parameter and M蠐 Nt, Nr) discrete valued symbols over an M-degree quadratic function. Then we employ integer programming which is a tree based branch-and-bound search algorithm to further reduce the complexity of the M-dimensional marginalization. Simulation results show that the proposed PGA-IP outperforms MMSE-SIC by about 5dB under heavily correlated channel with only several times of increased computational complexity. At the same time, with about 5% of the complexity of the exact PGA algorithm, the proposed PGA-IP only suffers marginal performance penalty.