Quadrotor unmanned aerial vehicles (UAVs) have emerged as ubiquitous and agile robots and data carriers within the framework of the future Internet of Things (IoT) and mobile wireless networks. Yet, the insufficient onboard battery necessitates the optimization of energy consumption for both the UAV and IoT devices while ensuring that communication requirements are met. This paper therefore proposes a more accurate and mathematically tractable model for characterizing a UAV’s energy consumption concerning desired trajectories. This nonlinear model takes into account the UAV’s dynamics, brushless direct current (BLDC) motor dynamics, and aerodynamics. To optimize the communication time between IoT devices and the UAV, IoT devices are clustered using a modified GAK-means algorithm, with dynamically optimized communication coverage radii. Subsequently, a fly–circle–communicate (FCC) trajectory design algorithm is introduced and derived to conserve energy and save mission time. Under the FCC approach, the UAV sequentially visits the cluster centers and performs circular flight and communication. Transitions between cluster centers are smoothed via 3D Dubins curves, which provide physically achievable trajectories. Comprehensive numerical studies indicate that the proposed trajectory planning method reduces overall communication time and preserves UAV battery energy compared to other benchmark schemes.