Code acquisition in DS/CDMA systems is usually conducted using a correlator. However, in a multiuser access interference (MAl) environment, its performance is seriously degraded. The adaptive filtering scheme has been proposed to overcome this problem. Although this approach is effective, it requires high computational complexity. This paper proposes a multirate adaptive filtering scheme to alleviate this problem. The proposed scheme uses two adaptive filters operated in different rates. Due to downsampling operations, the computational complexity of the adaptive filters can be effectively reduced. We also theoretically analyze the mean acquisition time and the acquisition error probability. Simulations show that while the proposed scheme can have better performance, its computational complexity is only half of the conventional adaptive filtering method.