A multiuser detector was developed for fast fading code-division multiple-access systems by representing the channels as a system with the multiplicative noise (SMN) model and then using the known optimal filtering algorithm for the SMN for multiuser detection (MUD). This multiuser detector allows the channel response to be stochastic in one symbol duration, which can be regarded as an effective method of MUD for fast fading CDMA systems. Performance analyses show that the multiuser detector is theoretically valid for CDMA systems over fast fading channels. Simulations show that the multiuser detector performs better than the Kalman filter-based multiuser detector with a faster convergence rate and lower bit error rate.