A training-based vector channel estimation method has been proposed for single-user code-division multiple access (CDMA) systems in fast-varying correlated multipath fading channels. In this paper, we extend it in an iterative way to multiuser multiple-input multiple-output (MIMO) CDMA systems where both the transmitter and receiver have multiple antennas. In the training period, we propose to add the minimum mean square error (MMSE) front end before channel estimation to suppress multiuser interference (MUI) from substreams with difference spreading codes, so then we can get good initial vector channel estimation for each user. In the data transmission period, we proposed to add MMSE/parallel interference cancellation (PIC) front end to suppress MUI, interference suppression, and vector channel estimation in an iterative way. The perfect channel estimation is assumed in Liu et al., and the inter-play between channel estimation and multiuser detection is not discussed either. On the contrary, the novelty of the proposed method is that we add MMSE/PIC front end (in addition to matched filter) before channel estimation and we repeatedly switch between MMSE/PIC front end and channel estimation.