Unmanned Aerial Vehicle ad hoc networks (UAANETs) are originally designed to work in a cooperative environment. These networks are vulnerable to a wide range of attacks due to the lack of predefined infrastructure and the dynamic topology. Security in ad hoc networks, in general, is handled through authentication and encryption. This can be considered as a heavy way to protect the network due to the lack of resources in the nodes. However, trust can be introduced to address a light weight solution for some security issues. In this paper, we focus on the concept of decentralized trust to design an efficient and trustful routing protocol, and ensure stable routes between nodes in spite of the rapidly changing topology, and to provide a mechanism for detecting malicious incorrect packet forwarding attacks. The proposed light-weight trust-quality routing protocol (TQAODV) provides two main functionalities: monitoring the behavior of the neighboring nodes and computing the trust value based on the historical information in the network. Moreover, the new proposed model reduces routing overhead and route discovery frequency. The simulations we used in NS-2 show that the proposed routing scheme gives better performance against attacks compared to the traditional Ad-hoc On-demand Distance Vector (AODV), and improves the packets delivery ratio with about 15%, routing packets overhead and average delay with about 20%, compared to trust AODV.