Cognitive radio (CR) technology is regarded as a promising solution by enabling unlicensed users to exploit the licensed spectrum unused by the licensed user in an opportunistic manner. Since in a mobile CR network, if unlicensed users move away from each other, their relative distance changes. Thus, the unlicensed user transmission power needs to be adapted to maintain their communications. In the meantime, since the spectrum availability is location-varying, the unlicensed users may also need to perform spectrum handoffs to avoid harmful interference to PUs caused by the increase of the transmission power. In this paper, in order to address this problem, a joint power adaptation and spectrum handoff scheme is proposed in mobile CR networks. The throughput of the unlicensed user transmission is used to evaluate the performance of the proposed algorithm. Simulation results show that our proposed algorithm achieves very high throughput when the unlicensed receiver is mobile. To the best of our knowledge, this is the first paper that jointly investigates both the power adaptation and the spectrum handoff in mobile CR ad hoc networks.