In the localized Discrete Fourier Transform-Spread-Orthogonal Frequency Division Multiplexing (DFT-S-OFDM) uplink cooperative system, multiple carrier frequency offsets (MCFO), arising from the nodes' separate oscillators and Doppler spreads, drastically degrade the performance of the receiver. To solve the problem, this letter proposes an efficient MCFO compensation method which fully exploits the diversity gain of space frequency block coded (SFBC) and the characteristic of inter-carrier interference (ICI). Moreover, the bit error ratio (BER) lower bound of the proposed algorithm is theoretically derived. Simulation results validate the theoretical analysis and demonstrate that the proposed MCFO compensation method can achieve robust BER performance in a wide range of MCFO in the multipath Rayleigh fading channel.