In this work, we proposed user selection strategies for downlink of multiple input and multiple output (MIMO) cognitive radio (CR) network. Underlay CR secondary users (SUs) are selected by cognitive base station (CBS) to share subchannel with primary users (PUs). It is assumed that the cross interference channel from cognitive radio base station to PUs is not known. CBS selects underlay SUs based on the knowledge of SUs transmission channels in order to reduce the interference from base station to PUs. We propose and evaluate user selection schemes with low computational complexity and best-effort interference mitigation to PUs.