Recently, attention on wireless communications has been shifted from multiple-input multiple-output (MIMO) systems to multiuser MIMO (MU-MIMO) systems, which serve several users simultaneously in frequency and time. For a system with multiantenna users, block diagonalization (BD) is a technique, where multiuser interference can be completely canceled. For realizing the BD algorithm, the base station should know the accurate channel state information (CSI) of users. However, the CSI fed back to the base station becomes outdated due to the time-varying nature of the channels. Channel prediction is an efficient approach to combat the performance degradation due to feedback delay in single user MIMO system, but in a BD system, the multiuser interference will still remain. In this paper, we analyse the effects of the imperfect CSI caused by feedback delay on BD MIMO downlink system with channel prediction. The result is that the interference will be proportional to the mean square error (MSE) of predicted CSI. We also propose a robust scheme for this kind of systems.