Abstract-A robust distributed optimal power control (RDPC) scheme under worst case condition is proposed to make primary users (PUs) receive minimum interference generated from all secondary users (SUs) in underlay cognitive radio networks (CRNs). The strategy considers the transmit power of each SU below the maximum allowable power of the devices and interference plus noise ratio (SINR) of each SU under the minimum threshold. Simulation illustrate thatthe RDPC can lead SUs to reduce the interference to PUs, and simultaneously the better meet quality of service (QoS) requirement of SUs in comparison with the distributed power control algorithm (DPC) and the traditional iterative water filling algorithm (IWFA) in timevarying channel environment.Index Terms-cognitive radio networks, robust distributed power control (RDPC), worst case condition