In this paper, we propose a distributed power control algorithm based on PID control and dynamic constraint condition for cognitive radio networks. In our proposed algorithm, at first, each transmitter in secondary networks receives the feedback information about signal-to-interference plus noise ratio (SINR) from its corresponding receiver. Based on the information, the transmitter derives the transmitted power with PID control in order to satisfy the quality of service (QoS) constraints in secondary networks. Then, the transmitter decides the actual transmitted power according to a constraint condition in addition to the derived power. This constraint condition is effective for avoiding the interference with primary networks. Since the constraint condition affects the performance of our proposed method significantly, we propose an effective update algorithm. In the update algorithm, the transmitter changes the constraint condition by comparing the derived transmitted power with both the maximum interference power tolerance and the target SINR. We evaluate the performance of our proposed algorithm with simulation. Numerical examples show that our proposed algorithm is effective for the power control in cognitive radio networks.