Multiuser MIMO (MU MIMO) communications have attracted considerable attention in the last years since these systems are able to offer the higher link capacity of MIMO systems as long as channel state information (CSI) is available at the transmitter, so that the spatial properties of the channel can be exploited by precoding. However, the time varying nature of the channel and other transmissions constraints may cause CSI to be outdated, degrading the performance of the system. Considering this scenario, channel prediction can provide up-to-date channel CSI and reduce the performance loss. This paper presents a channel predictor based on the set-membership affine projection (SM-AP) filtering as way to compensate the outdated CSI. A realistic standardized channel model is used to evaluate the influence of the proposed predictor on two classical precoding schemes of the MIMO broadcast channel of a multiuser scenario, namely zero-forcing vector perturbation. The performance of the predictor is compared to the well-known adaptive algorithms normalized least mean squares (NLMS) and recursive least squares (RLS). Simulation results show that the SM-AP predictor has lower computational cost and superior performance when compared to the classical algorithms.