Multi-Carrier Code Division Multiple Access (MC-CDMA) is one of candidates for the next generation wireless communication systems. In an uplink, the MC-CDMA system suffers from the different access timing (asynchronous transmission), the different fading, and the different frequency offsets of each active user. In this paper we analyze the effects of the frequency offset compensation with MMSE-MUD (minimum mean square error based multi-user detection) for MC-CDMA in a quasi-synchronous uplink. We consider the MC-CDMA system with two subcarrier mapping schemes, the continuous mapping scheme and the discrete mapping scheme. From our theoretical analysis and computer simulation, we show that the MMSE-MUD can compensate the different frequency offsets among users. We also show that the MMSE-MUD significantly improves the bit error rate (BER) for the MC-CDMA system with the continuous mapping scheme.