In the cognitive radio system, one cognitive user (secondary user) has a limited capability of detecting the licensed primary user because of the hidden terminal problem; therefore, cooperation of the cognitive users is required to improve the spectrum sensing performance. Nevertheless, the cognitive users do not transmit data or voice all the time, and the idle cognitive users may consume massive spectrum sensing power instead of communication power. Therefore, we propose a partial FFT spectrum sensing method to reduce the cooperative spectrum sensing power. Moreover, we present two techniques, called detection result prediction (DRP) and decision result modification (DRM), to increase the detection accuracy based on the frequency-domain correlation and detection diversity. Simulation results show that the proposed technique can not only save about 50% computational complexity but also improve the detection performance.