We propose an iterative multiuser detector for turbo-coded synchronous and asynchronous direct-sequence CDMA (DS-CDMA) systems. The receiver is derived from the maximum a posteriori (MAP) estimation of the single user's transmitted data, conditioned on information about the estimate of the multiple-access interference (MAI) and the received signal from the channel. This multiple-access interference is reconstructed by making hard decisions on the users' detected bits at the preceding iteration. The complexity of the proposed receiver increases linearly with the number of users. The proposed detection scheme is compared with a previously developed one. The multiuser detector proposed in this paper has a better performance when the transmitted powers of all active users are equal in the additive white Gaussian noise (AWGN) channel. Also, the detector is found to be resilient against the near-far effect.