An ad-hoc Learning Automata-based protocol for wireless LANs, capable of operating efficiently under bursty traffic conditions, is introduced. According to the proposed protocol, the mobile station that is granted permission to transmit is selected by means of Learning Automata. The Learning Automaton takes into account the network feedback information in order to update the choice probability of each mobile station. The proposed protocol is compared via simulation to TDMA under bursty traffic conditions and is shown to exhibit superior performance even when the network feedback is noisy.