Unmanned aerial vehicle (UAV)-assisted relaying and mobile edge computing (MEC) networks is a popular and promising technology to provide high-quality computation service to ground users (GUs). However, prior works on UAV-assisted relaying and MEC networks do not consider the complicated channel conditions in urban environment. Furthermore, the optimization of computation efficiency, defined as the ratio of computation resources (in terms of CPU frequency) and energy consumption, is not studied in prior works. In this work, we consider an UAV-assisted relaying and MEC networks composed of GUs, two MEC servers carried by one rotary-wing UAV and one base station (BS), respectively. Meanwhile, we consider the probabilistic Line-of-Sight (LoS) channel model and the Rician fading model in urban environments to make the channel model more practical and accurate to urban environments. Further, we aim to solve the maximization problem of computation efficiency by jointly optimizing computation resources, computation offloading, bandwidth and UAV trajectory. For the non-convex formulated problem, we proposed an algorithm based on the Dinkelbach’s method, the block coordinate descent (BCD) method and successive convex approximate (SCA) technique. Numerical results demonstrate that the proposed scheme can efficiently improve the computation efficiency compared to other traditional schemes in the practical simulation environment.