In this paper, a pilot-assisted minimum mean square error (MMSE) multiuser channel estimation algorithm is proposed for quasi-synchronous code-division multiple-access (CDMA) systems that undergo frequency-selective channel fading. The frequency-selective multiuser fading channel is represented as a symbol-wise time-varying chip-spaced tapped delay line filter with correlated filter taps. The multiuser channel tap coefficients at pilot symbol positions are estimated under the MMSE criterion with the help of the channel intertap correlation matrix, which is determined by the combined effects of the physical fading channel, transmit filter, and receive filter. In the development of the estimation algorithm, the channel intertap correlation matrix is deemed as an essential factor, and a novel iterative method is proposed for the joint estimation of the channel intertap correlation and filter tap timing based on the received pilot samples. Simulations show that the information of the channel intertap correlation is critical to the performance of the channel estimation, and the channel taps at different delays cannot be assumed uncorrelated for CDMA systems experiencing frequency-selective fading.