Routing protocols based on trust mechanisms have been widely investigated for wireless sensor networks, and the works have achieved good results, while there are few works on trusted routing for underwater acoustic networks (UANs). However, trust-aware routing is the key to improving the packet delivery rate and the energy efficiency of UANs. Therefore, inspired by the theory of trust evaluation, a trust-aware and fuzzy logic-based reliable layering routing protocol (TAFLRLR) is proposed. In the TAFLRLR protocol, to avoid the problem of the void area and improve the transmission reliability, the candidate nodes of the next-hop forwarding nodes are determined according to the layers of neighbor nodes. Moreover, a fuzzy logic-based trust evaluation mechanism (FLTEM) is provided, which employs the fuzzy comprehensive evaluation decision model to calculate the comprehensive trust value for underwater sensor nodes. Further, the node density of a candidate node and its comprehensive trust value are taken as the input of a fuzzy control system and the forwarding probability (FP) of the node is taken as the output, and the candidate node with the highest FP is selected as the best forwarding node. Simulation results illustrate the superiority and effectiveness of the TAFLRLR protocol in terms of energy efficiency, routing reliability, and transmission reliability.