The ordered successive interference cancellation (OSIC) detector based on the minimum mean square error (MMSE) criterion has been proved to be a low-complexity detector with efficient bit error rate (BER) performance. As the well-known MMSE-Based OSIC detector, the MMSE-Based vertical Bell Laboratories Layered Space-Time (VBLAST) detector, whose computational complexity is cubic, can not attain the minimum BER performance. Some approaches to reducing the BER of the MMSE-Based VBLAST detector have been contributed, however these improvements have large computational complexity. In this paper, a low complexity MMSE-Based OSIC detector called MMSE-OBEP (ordering based on error probability) is proposed to improve the BER performance of the previous MMSE-Based OSIC detectors, and it has cubic complexity. The proposed detector derives the near-exact error probability of the symbols in the MMSE-Based OSIC detector, thus giving priority to detect the symbol with the smallest error probability can minimize the error propagation in the MMSE-Based OSIC detector and enhance the BER performance. We show that, although the computational complexity of the proposed detector is cubic, it can provide better BER performance than the previous MMSE-Based OSIC detector.