This paper proposes a novel UAV-based edge computing system for augmented reality (AR) applications, addressing the challenges posed by the limited resources in mobile devices. The system uses UAVs equipped with edge computing servers (UECs) specifically to enable efficient task offloading and resource allocation for AR tasks with dependent relationships. This work specifically focuses on the problem of dependent tasks in AR applications within UAV-based networks. This problem has not been thoroughly addressed in previous research. A dual network architecture-based task offloading (DNA-TO) algorithm is proposed, leveraging the DNA framework to enhance decision-making in reinforcement learning while mitigating noise. In addition, a Karush–Kuhn–Tucker-based resource allocation (KKT-RA) algorithm is proposed to optimize resource allocation. Various simulations using real-world movement data are conducted. The results indicate that our proposed algorithm outperforms existing approaches in terms of latency and energy efficiency.