Linear multiuser detection is demanded in a CDMA mobile radio system while always with an unacceptable complexity. To overcome the drawback, we propose a low complexity zero forcing (ZF) multiuser detection scheme, namely block Fourier transform ZF (BFT-ZF). In the proposed transmitter, the only difference from the traditional one is that a cyclic prefix (CP) is added into each transmission unit. Then, the system transfer matrix can be equivalent to a block-circulant matrix by utilizing the information from CP. And, it is easy to be block-diagonalized by block fast Fourier transforms. Thus, on the receiver side, the complexity of matrix inversion decreases dramatically. Accordingly, the total complexity of the ZF receiver is obviously reduced. The analysis and simulation results show that the proposed scheme is able to achieve almost the same bit error rate (BER) performance with much less complexity than the traditional ZF multiuser detector