In mobile ad hoc networks (MANETs), providing reliable and stable communication paths between wireless devices is critical. This paper presents a fuzzy logic stable-backbone-based multipath routing protocol (FLSBMRP) for MANET that provides a high-quality path for communication between nodes. The proposed protocol has two main phases. The first phase is the selection of candidate nodes using a fuzzy logic technique. The second phase is the construction of a routing backbone that establishes multiple paths between nodes through the candidate nodes, thus forming a routing backbone. If any candidate node in the path fails due to a lack of bandwidth, residual energy or link quality, an alternate path through another candidate node is selected for communication before the route breaks, because a candidate node failure may lead to a broken link between the nodes. Simulation results demonstrate that the proposed protocol performs better in terms of the packet delivery ratio, overhead, delay and packet drop ratio than the major existing ad hoc routing protocols.