This paper proposes a non-linear overloaded MIMO detector that outperforms the conventional soft-input maximum likelihood detector (MLD) with less computational complexity. We propose iterative log-likelihood ratio (LLR) estimation and multi stage LLR estimation for the proposed detector to achieve such superior performance. While the iterative LLR estimation achieves better BER performance, the multi stage LLR estimation makes the detector less complex than the conventional soft-input maximum likelihood detector (MLD). The computer simulation reveals that the proposed detector achieves about 0.6dB better BER performance than the soft-input MLD with about half of the soft-input MLD's complexity in a 6×3 overloaded MIMO OFDM system.