In this letter, we study the power control of a cognitive radio (CR) network, where the secondary user (SU) is allowed to share the spectrum with the primary user (PU) only if the signal to interference plus noise ratio (SINR) at the PU is higher than a predetermined level. Both PU fixed power control and PU adaptive power control are considered. Specifically, for the PU adaptive power control, the PU will cooperate with the SU by transmitting with adaptive power. The optimal power control schemes for the SU to maximize the SU throughput under the PU SINR constraint are derived. It is shown that the SU throughput achieved by the optimal power control with the PU adaptive power control is a significant improvement over the optimal power control with the PU fixed power control, especially under high power constraint and low SINR constraint.