In conventional terrestrial cellular networks, mobile devices at the cell edge often suffer from poor channel conditions, and thus unmanned aerial vehicles (UAVs) are introduced in recent years to improve the reliability of communication links. However, with the rapid development of Internet of Things (IoT) technology, the emerging IoT applications have blooming demands for high computation capacity from the resource-constrained IoT mobile devices (IMDs), motivated by which, mobile edge computing has been envisioned as an appealing solution to the resource bottleneck problem of IMDs. In order to cope with poor communication performance and high computation demands of cell-edge IMDs, we in this paper leverage UAV-aided edge computing to collaboratively assist computation offloading, taking account of the limited battery life of both IMDs and the UAV. We investigate a joint optimization problem of collaborative computation offloading, bandwidth portion, bit allocation, and UAV trajectory design, aiming to minimize the weighted energy consumption of IMDs and the UAV. Extensive numerical results validate the necessity of introducing UAV-aided edge computing to cellular networks, and the advantages of our proposed scheme on energy savings.