Power control (PC) is a key solution to enable spectrum sharing between secondary users (SUs) and primary users (PUs). However, previous research lacks sensing uncertainties for the status of PUs. In this article, we focus on the PC problem for a cognitive relay network under the spectrum sensing uncertainties to minimize the total bit error rate (BER) of SUs under the constraints of maximum transmit power budgets, signal-to-interference-and-noise ratio (SINR) constraints, and interference requirements to provide protection for PUs. We first formulate the interference model by taking sensing uncertainties into account, while the worst-channel-state-information (worst-CSI) PC algorithm is introduced to limit the BER of SUs, which only needs to operate the algorithm in one link whose CSI is worst. And a cooperative spectrum sensing (CSS) strategy is considered to optimize the sensing performance. To deal with the optimization problem, the original min-max BER problem is converted into an equivalent max-min SINR problem solved by Lagrange dual decomposition method. Finally, simulation results are presented to indicate that our proposed algorithm can obtain good BER performance and guarantee quality of service of PU.