In this paper, three issues concerning the linear adaptive receiver using the LMS algorithm for single-user demodulation in direct-sequence/code-division multiple-access (DS/CDMA) systems are considered. First, the convergence rate of the LMS algorithm in DS/CDMA environment is considered theoretically. Both upper and lower bounds of the eigenvalue spread of the autocorrelation matrix of receiver input signals are derived. It is cleared from the results that the convergence rate of the LMS algorithm becomes slow when the signal power of interferer is large. Second, fast converging technique using a prefilter is considered. The LMS based adaptive receiver using an adaptive prefilter adjusted by a Hebbian learning algorithm to decorrelate the input signals is proposed. Computer simulation results show that the proposed receiver provides faster convergence than the LMS based receiver. Third, the complexity reduction of the proposed receiver by prefiltering is considered. As for the reduced complexity receiver, it is shown that the performance degradation is little as compared with the full complexity receiver.