In this paper, we design an efficient resource-allocation strategy for a multiuser multiple-input-multiple-output (MU-MIMO) rateless-coded cognitive radio network (CRN) with quality-of-service (QoS) provisioning. We consider a limited feedback MU-MIMO CRN, where zero-forcing beamforming (ZFBF) is performed under imperfect channel state information (CSI) at a cognitive base station to mitigate both inter- and intranetwork interferences. To minimize the total feedback amount while satisfying the interference constraint and QoS requirements simultaneously, we propose to adaptively adjust the transmit power, select the transmission mode, and choose the feedback codebook size according to the interference constraint, CSI, and QoS requirements. The optimization problem is shown to be an integer programming problem, and we propose a heuristic algorithm that can provide an optimal solution for most practical scenarios. Results show that our resource-allocation strategy can decide the feedback amount and transmission mode adaptively based on the delay requirements.