The maximum–minimum-throughput-based power assignment (MMTPA), which results in the maximum–minimum throughput among all secondary users (SUs) while assuring the quality of service (QoS) of each primary user (PU), is proposed for multiple-input–multiple-output (MIMO) systems in cognitive radio (CR) networks. We first derive the capacity bound of the MIMO system under cochannel interference and use this capacity bound to quantify the throughput. Instead of employing the traditional optimization technique, we present a proposition to simplify the optimization of the power assignment. In particular, in the uplink of the infrastructure-based CR network, the problem can be reduced so that the MMTPA only has to optimize the transmit power of the representative SU and keep the ratio of the transmit power of each SU to that of the representative SU constant. For comparison, we also propose two other power assignments, namely, the equal power assignment (EPA) and the iterative power control (IPC). As expected, we found from simulation results that MMTPA outperforms EPA and IPC in the minimal throughput among all SUs.