A two-hop low-altitude relay communication system design is proposed in this work. Due to the remarkable height and location of antennas in the studied relay, both the channel between low-altitude relay and a source node and the channel between the relay and a destination node are primarily modeled as line-of-sight channel, direct transmission channel between the source node and the destination node is Rayleigh fading and has a larger path loss exponent than two. So the low-cost low-altitude relay network should have potential to support higher data rates than that of the direct transmission, which is applied in scenarios like emergency communications and rural communication. To improve the date rate performance of the conventional half-duplex relaying mode, full-duplex relaying mode is considered where the capacity is restricted by the residual self-interference. The computer simulation results show that the capacity of the full-duplex mode is significantly better than that of half-duplex relaying mode. However with the enhancement of residual self-interference, the capacity of full-duplex relaying mode will be worse than those of half-duplex relaying mode and direct transmission mode.