LoRa, due to its advantage of long-range communication capability, is promising for Internet of Things (IoT) and space-air-ground communications. However, the conventional MAC protocol used with LoRa is classified as an Aloha-based algorithm, which leads to drastic decrease in throughput when a huge amount of end-devices try to access the network. To achieve stable and high throughput of LoRa, we propose a design to combine the distributed queueing (DQ) and in-band-full-duplex (IBFD) technologies. The usage of DQ mechanism is benefit for fast collision resolution, while the IBFD-enabled gateway helps to reduce the heavy-control-overhead of DQ. The designs of access procedure and frame structure are discussed in detail. The outage probability and average throughput are evaluated under imperfect self-interference cancellation. Also, a mathematical programming method is developed to optimize the spreading-factor and code-rate. Numerical results show that our proposal gains an extra enhancement of 1.83-fold in throughput.