Traditional wireless security focuses on preventing unmanned aerial vehicle (UAV) communications from suspicious eavesdropping and/or jamming attacks. However, there is a growing need for governments to keep malicious UAV communications under legitimate surveillance. This paper first investigates a new surveillance paradigm for monitoring suspicious UAV communications via jamming suspicious UAVs. Due to the power consumption limitation, the choice of eavesdropping and jamming will reflect the performance of the UAVs communication. Therefore, the paper analyses the UAV's eavesdropping and jamming models in different cases, and then proposes the model to optimize the data package in the constraints of lower power consumption, which can be solved by the proposed selection policy. The simulation results validate our proposed selection policy in terms of power consumption and eavesdropped packets. In different fading models, power consumption increases with time, regardless of distances, and our proposed policy performs better in Weibull fading channels in terms of eavesdropped packets.