Due to its lower peak-to-average power ratio (PAPR) compared with orthogonal frequency division multiple access (OFDMA), single carrier frequency division multiple access (SC-FDMA) has been recently accepted as the uplink multiple access scheme in the Long Term Evolution (LTE) of cellular systems by the Third Generation Partnership Project (3GPP). However, similar to OFDMA, carrier frequency offset (CFO) can destroy the orthogonality among subcarriers and degrade the performance of SC-FDMA. To mitigate the effect of CFOs, we propose a combined minimum mean square error frequency-domain equalization (MMSE-FDE) and interference cancellation scheme. In this scheme, joint FDE with CFO compensation (JFC) is utilized to obtain the initial estimation for each user. In contrast to previous schemes, where the FDE and CFO compensation are done separately, in JFC, the MMSE FDE is designed to suppress the MUI after CFO compensation. To further eliminate the MUI, we combine JFC with parallel interference cancellation (PIC). In particular, we iteratively design the MMSE FDE equalizer to suppress the remaining MUI at each stage and obtain better estimation. Simulation results show that the proposed scheme can significantly improve the system performance.