Multi carrier code division multiple access (MC-CDMA) system is a promising multi carrier modulation (MCM) technique for high data rate wireless communication over frequency selective fading channels. MC-CDMA system is a combination of code division multiple access (CDMA) and orthogonal frequency division multiplexing (OFDM). The OFDM parts reduce multipath fading and inter symbol interference (ISI) and the CDMA part increases spectrum utilization. Advantages of this technique are its robustness in case of multipath propagation and improve security with the minimize ISI. Nevertheless, due to the loss of orthogonality at the receiver in a mobile environment, the multiple access interference (MAI) appears. The MAI is one of the factors that degrade the bit error rate (BER) performance of MC-CDMA system. The multiuser detection (MUD) and turbo coding are the two dominant techniques for enhancing the performance of the MC-CDMA systems in terms of BER as a solution of overcome to MAI effects. In this paper a low complexity iterative soft sensitive bits algorithm (SBA) aided logarithmic-Maximum a-Posteriori algorithm (Log MAP) based turbo MUD is proposed. Simulation results show that the proposed method provides better BER performance with low complexity decoding, by mitigating the detrimental effects of MAI.