Reliable routing of packets in a Mobile Ad Hoc Network (MANET) has always been a major concern. The open medium and the susceptibility of the nodes of being fault-prone make the design of protocols for these networks a challenging task. Faults in these networks may occur either due to the failure of nodes or due to their reorganisation in the network. These faults can eventuate to packet loss, which degrades the performance of any routing protocol. In this paper, we propose a routing algorithm, named as learning automata based fault-tolerant routing algorithm (LAFTRA), which is capable of routing in the presence of faulty nodes in MANETs using multi-path algorithm. In this work, we have used Learning Automata (LA) for optimizing the selection of paths from multipath routing. The results of simulation of our protocol using network simulator 2 (NS-2) shows the increase in packet delivery ratio and decrease in overhead compared to the existing protocols.