We propose a new multiuser FBMC that performs cyclic-shift on discrete Fourier transform-spread data symbols prior to FBMC modulation. The interference between frequency asynchronous users' adjacent resource blocks (RBs) is minimized. In the receiver, the RBs' cyclic shift values are detected in a simple blind manner. As the inter-user frequency offset range increases, the conventional FBMC schemes break down, and the BERs saturate at high SNR. Moreover, with inter-user power differences, the BERs (bit error rates) saturate to an unacceptable level. In contrast, the proposed FBMC retains the same slope of the BER curves as that of the interference-free case.