In underwater acoustic communication, the Doppler shift can severely degrade demodulation performance. In addition, multipath signals can have the Doppler shifts that are different from that of a direct signal. Although conventional signal processing in underwater acoustic communication can deal with multipath signals with the Doppler shifts equal to that of the direct signal, they cannot sufficiently deal with multipath signals with different Doppler shifts. In this paper, we provide a mathematical description of how multipath signals with the different Doppler shifts degrade demodulation performance. Moreover, signal processing, which suppresses the effects of such multipath signals, has been proposed. In addition, to confirm the improvement due to the proposed processing, simulations of communication between a small surface vessel and an underwater vehicle were carried out in this study. The results show that the proposed processing yields a demodulation performance better than that of conventional processing. Furthermore, we investigated how the proposed processing improved the performance under some motional conditions. Finally, through simulations at various symbol rates, the motional and signal conditions under which the proposed processing can improve the performance efficiently are discussed.