Spectrum efficiency can be greatly improved through high-accuracy spectrum sensing in cognitive unmanned aerial vehicle (UAV) networks. However, the traditional centralized cooperative spectrum sensing (CCSS) methods are not applicable to the spectrum sensing of cognitive UAV networks, since the mobility of nodes and the dynamicity of network topology make it challenging to gather all the sensing information into a fusion center (FC) quickly enough. To overcome the challenge, this paper proposes a clustering-based distributed cooperative spectrum sensing (c-DCSS) scheme. Specifically, the considered cognitive UAV network is first clustered based on Max-Min distance clustering methods by jointly taking the position, velocity, and moving direction of UAVs in account, and then a two-stage fusion scheme is adopted to execute hierarchical sensing information fusion. Simulation results show that compared to the unclustered DCSS (u-DCSS) scheme, the proposed scheme significantly enhances the spectrum detection performance of cognitive UAV networks, especially when the number of UAV nodes is relatively large.