The core aim of this work is the maximization of the achievable data rate of the secondary user pairs (SU pairs), while ensuring the QoS of primary users (PUs). It is assumed that when PUs are present, the direct communications between SU pairs introduces intolerable interference to PUs and thereby SUs transmit signal using the cooperation of one of the SUs. In a brief, an adaptive cooperative strategy for MIMO cognitive radio networks is proposed. At the presence of PUs, the issue of joint relay selection and power allocation in Underlay MIMO Cooperative Cognitive Radio Networks (U-MIMO-CCRN) is addressed. The optimal approach for determining the power allocation and the cooperating SU is proposed. Due to high complexity of the optimal approach, a low complexity approach is further proposed and it is proved, using simulations, that performance loss due to the low complexity approach is only about 14%.