This paper proposes an adaptive power allocation scheme in cognitive radio system under MIMO fading channel. In the spectrum-sharing system, the secondary user (SU) can use the primary user's (PU) spectrum band under some limitations. In this research, we consider that the SU's transmission power has to be limited to ensure an acceptable effect on the primary's receiver, meanwhile the QoS of the primary user's should be guaranteed. Under the limitations of average and peak received-power at the side of PU's receiver, we get the optimum power allocation scheme of SU, and the channel capacity is adopted as the metric of the system performance. Finally, we verify the theoretical results through numerical simulations.