This paper considers a swarm of Unmanned Aerial Vehicles (UAVs) managed by a ground station.These UAVs may experience highly varying channel gains and collisions when they transmit to the ground station. To this end, we introduce a novel Learning Medium Access Control (L-MAC) for multi-rate UAVs and equip the ground station with Successive Interference Cancellation (SIC) capability. The ground station uses L-MAC to learn a Time Division Multiple Access (TDMA) schedule/frame length that yields the highest throughput.UAVs, on the other hand, use L-MAC to learn the best transmission slot and data rate for a given frame length. Our extensive simulation results show that L-MAC achieves up to five times higher throughput as compared to the well-known Aloha protocol. Specifically, L-MAC achieves a throughput of 500 kbps as compared to 100 kbps for Aloha.In comparison, Aloha with SIC achieves a throughput of 300 kbps for the same network scenario. On the other hand, the throughput of L-MAC is as most half that of the case when the ground station has perfect channel state information.Our results also show that the frame length is always set to around 60–75% of the total number of UAVs.